Gap between the Lower and Upper Bounds for the Iteration Complexity of Interior-Point Methods
ISBN 978-979-95093-9-0
INf; S
P ｬｦＩＨｾｉ＠
Published By
•
.. .. .
'
,..
....
..
I -,
ISBN : 978-979-95093-9-0
PROCEEDINGS
155 2013
International Seminar on Sciences 2013
"Perspectives on Innovative Sciences"
Bogar 15-17 November 2013
IPB International Convention Center
Published by
Faculty of Mathematics and Natural Sciences
Bogar Agricultural University
Copyright© 2014
Faculty of Mathematics and Natural Sciences, Bogor Agricultural University
Proceedings of International Seminar on Sciences 2013 "Perspectives on Innovative Sciences"
Bogor 15-17 November 2013.
Published by: FMIPA-IPB, Jalan Meranti Kampus IPB Dramaga, Bogor 16680
Telp/Fax: 0251 -8625481 /8625708
http://fmipa.ipb.ac.id
ix + 395 pages
ISBN: 978-979-95093-9-0
ii
Boa rd of Editors
PROCEEDINGS
INTERNATIONAL SEMINAR ON SCIENCES 2013
Chief Editor:
Endar H. Nugrahani
Managing Editor:
lndahwati
Nisa Rachmania
Managing Team:
Wisnu Ananta Kusuma
Ali Kusnanto
International Scientific Committee:
Manabu D. Yamanaka (Kobe University, Japan)
Kanaya (Nara Institute of Science and Technology, NAIST, Japan)
Ken Tanaka (Toyama University, Japan)
Daniel Oosgood (Columbia University, USA)
Emmanuel Paradis (lnstitut de Recherche pour le Developpement, IRD, France)
Rizaldi Boer (Begor Agricultural University, Indonesia)
Antonius Suwanto (Begor Agricultural University, Indonesia)
National Reviewer:
Kiagus Dahlan
Tania June
Sri Sugiarti
Miftahudin
Anja Meryandini
Imas Sukaesih Sitanggang
Farit Mochamad Afendi
Paian Sianturi
Husin Alatas
Heru Sukoco
Charlena
Suryani
iii
FOREWORD
The International Seminar on Sciences 2013, which had the main theme "Perspectives on Innovative
Sciences", was organized on November 15 h -1 ih, 2013 by the Faculty of Mathematics and Natural
1
Sciences, Bogor Agricultural University. This event aimed at sharing knowledge and expertise, as well
as building network and collaborations among scientists from various institutions at national and
international level.
Scientific presentations in this seminar consisted of a keynote speech, some invited speeches, and
about 120 contributions of oral and poster presentations. Among the contributions, 66 full papers
have been submitted and reviewed to be published in this proceeding. These papers were clustered in
four groups according to ou r themes:
A. Sustainability and Science Based Agriculture
B. Science of Complexity
C. Mathematics, Statistics and Computer Science
D. Biosciences and Bioresources
In this occasion, we would like to express our thanks and gratitude to our distinguished keynote and
invited speakers: Minister of Science and Technology, Prof. Manabu D. Yamanaka (Kobe University,
Japan), Prof. Kanaya (Nara Institute of Science and Technology, NAIST, Japan), Prof. Ken Tanaka
(Toyama University, Japan), Emmanuel Paradis, PhD. (lnstitut de Recherche pour le Developpement,
IRD, France), Prof. Dr. Ir. Rizaldi Boer, MS (Bogor Agricultural University), and Prof. Dr. Ir. Antonius
Suwanto, M .Sc. (Bogar Agricultural University).
We would like also to extend our thanks and appreciation to all participants and referees for the
wonderful cooperation, the great coordination, and the fascinating efforts. Appreciation and special
thanks are addressed to our colleagues and staffs who help in editing process. Finally, we
acknowledge and express our thanks to all friends, colleagues, and staffs of the Faculty of
Mathematics and Natural Sciences IPB for their help and support.
Bogar, March 2014
The Organizing Committee
International Seminar on Sciences 2013
iv
Table of Content
Page
Board of Editors
Foreword
Table of Content
A. Sustainability and Science Based Agriculture
111
i \I
v
Development of a natural rubber dryer Based on muh1 energy
resources (biomass. solar and wind)
Didin Suwardin, Afrizal
Vachlepi. Mili Pubaya, Sherly
Hanifarianty
3
2
Characterization ofHDTMABr-modified Na1ural Zeolite and its
Application in Cr(VI) Adsorption
Budi Riza Putra. Laiifah K
Darusman, Eti Rohaeti
7
3
Wulan Tri Wahyuni, Latifah K
Potency of Andrographis paniculata, Tinospora crispa, and
Darusman. Rona Jutama
Combination Extract as
a-Glucosidase Inhibitor and Chromatographic Fingerprint Profile
of the Extracts
17
4
Deliana Dahnum, Dyah Styarini,
Utilization of Frond Palm Oil as Second Generation Bioethanol
Production using Alkaline Pretreatment and Separated Hydrolysis Sudiyarmanto, Muryanto.
Haznan Abimanyu
and Fermentation Method
21
5
Pretreatment of Grass Biomass with Biological Process for
Efficient Hydrolysis
6
Alkaloid Compounds from Oil-Free Mahogany Seed (Swietenia Sri Mursiti, Sabirin Matsjeh,
macrophylla, King) and Hypoglycemia Effect of Mahogany Seed Jumina, and Mustafa
on The Rat (Rattus novergicus)
31
7
Utilization Of Vetiver Roots Waste Product as Strong, Low
Density, and Eco Friendly Material Pot
Galuh Suprobo, Tatang
Gunawan, Cynthia Andriani, Rio
Candra lslami
43
8
Green Products from Wastewater of Tempe Industry
Susanti Pudji Hastuti, Yofi
Bramantya Adi, Bary Fratarna.
Samuel Arunglabi,
Dewi KAK Hastuti, and Santoso
Sastrodiharjo
47
9
Saccharification of Oil Palm Empty Fruit Bunch After Alkaline
Pretreatment Followed by Electron Beam Irradiation for Ethanol
Production
Muryanto, Eka Triwahyuni,
Yanni Sudiyani
55
10
Isolation and Screening of Endophytic Bacteria from Bark of Raru Wasinton Simanjuntak, Heri
Plant (Tarrietia ribiginosa) and Their Potential for Bioetahnol
Satria, and Nurul Utami
Production
61
Desy Kumiawati, Muhamad
Natsir, Rahmi Febrialis and
Prima Endang Susilowati
27
v
II
Tht: Effect of Hypenension I lerbs Fonnula to Thi.' Kidne)
Functions
Agus Triyono. Saryanto
67
12
The Use of Activated Carbon from Ointaro Fruit-Shell (Cerbera
manghas) as an Adsorbent to Increase Water Quality
Armi Wulanawati, Kamella
Gustina and Djeni Hendra
71
13
Analysis of Active Compounds from Mangosteen Rind (Garcinia Fachrurrazie, Hall) Noviardi
mangostana L.) by Binding Affinity to The Androgen Receptor as
Anti-Prostate Cancer Drug Candidates
77
14
Antioxidant Activity from Formula of Jati Belanda (Guazuma
S) aefudin. Sulistiyani, Edy
ulmifolia Lamk.), Jambu Biji (Psidium guajava Linn.). and Salam Djauhari Purwakusumah
(Eugenia polyanrha Wight.) Leaves Extract
81
15
Diversity of Bacterial Mercury Reductase Resistance (mer A) from Prima Endang Susilowati, Sapto
Bombana Gold Mine
Raharjo, Rachmawati Rusdin.
Muzuni
87
16
Brake Fem (Pteris vittata) as a Prospective Heavy Metal
Accumulator: Utilization Potentials of Harvested Biomass and
Heavy Metal
Mochamad Taufiq Ridwan. Rike
Tri Kumala Dewi and Agung
I lasan Lukman
91
17
Protein Content Enhancement ofSpirulina platensis by
Phosphorus Limitation and Nitrogen Addition in Beef Carrie
Wastewater Medium
Irving Noor Arifin, lin
Supaninah Noer and Asri Peni
Wulandari
99
18
Development immobilized enzyme of white-rot fungus for
decolorization of RBBR
Ajeng Arum Sari and Sanro
Tachibana
103
19
Simple and Rapid Screening Method for Early Identification of
Salt Tolerant Foxtail Millet (Setaria italica L. Beauv)
Sintho Wahyuning Ardie, Nuru l
Khumaida, and Amin Nur
109
20
Synthesis of Silver Nanoparticles by Using Extracellular
Metabolites of Lactobacillus delbrueckii subsp. bulgaricus
Suryani, Ridho Pratama, Dimas
Andrianto
113
B. Science of Complexity
119
21
Regional Heat Capacity Changes due to Changes of Land Cover
Composition Using Landsat-5 TM Data
Winda Aryani, !dung Risdiyanto
121
22
Microbial Cellulolytic Isolation and Identification from Durian
Leather Waste
Hapsoh, Gusmawartati dan
Ujang Al Husnah
129
23
Predicting Water Surplus and Water Deficit in the Paddy Rice
Production Center in North Sulawesi Using the Water Balance
Model
Johanis H. Panelewen, Johannes
E. X. Rogi and Wiske
Rotinsulu3
135
24
Prediction of Oustfall Generation in Ambient Air over an
lnceptisol Soil Area
Arief Sabdo Yuwono, Lia
Amaliah
143
vi
25
Fitri Adilla, Lisman
Carboxymethyla1ton of Microfibrillated Cellulose to Improve
Thermal and Mechanical Properties of Polylactic Acid Composites Suryanegara. Suminar S.
Achmadi
149
26
Esterification of Microfibrillated Cellulose with Various
Anhydrides to Improve Thermal and Mechanical Properties of
Polylactic Acid Composite
Ajeng Ma\\ angi. Lisman
Suryanegara, Suminar S.
Achmad1
155
27
Thermal and Mechanical Properties Improvement of Pol) lactic
Acid-Nanocellulose Composites by Acetylation
Resty Dwi Andinie, Lisman
Suryanegara. Suminar S.
Achmadi
161
167
C. Mathematics, Sta tistics a nd Computer Science
28
Rado Yendra, Ari Pani Desvina,
The comparison spatial distribution observed. cstimatated using
Neyman-Scon Rectangular Pulse Method (NSRP}, and simulation Abdul Aziz Jemain
for mean of one-hour rain and probability of 24-hour rain
169
29
Optimal VAR Injection Based on Neural Network Current State
Estimator for 20kV Surabaya Electrical Distribution System
Dimas Fajar Uman P, Ontoseno
Penangsang, Adi Soeprijanto
175
30
Fire-Fighting Robot Navigat ion System Using Wall Following
Algorithm and Fuzzy Logic
Karlisa Priandana. Erwin M Y
Chriswantoro, Mushthofa
181
31
Analysis and Solving of Outliers in Longitudinal Data
Viani Eminita, lndahwati.
Anang Kumia
187
32
Implementation of Flowers and Ornamental Plants Landscape
Information System using Cloud Computing Technology
Meuthia Rachmaniah and
lswarawati
193
33
Cluster Information of Non-sampled Area in Small Area
Estimation with Non-normally Distributed Area Random Effects
and Auxiliary Variables
Rahma Anisa, Anang Kumia,
lndahwati
199
34
Study of Overdispersion for Poisson and Zero-Inflated Poisson
Regression on Some Characteristics of the Data
Lili Puspita Rahayu, Kusman
Sadik, lndahwati
203
35
The Effect of Two-Way and Three-Way Interaction of Perceived
Rewards on the Relationship Quality
Enny Kristiani, Ujang
Sumarwan, Lilik Noor Yulianti
& Asep Saefuddin
209
36
Implementation of Inverse Kinematics for the Coordination
Control of Six Legged Robot
Wulandari, Karlisa Priandana,
Agus Buono
213
37
Detection ofC Code Plagiarism by Using K-Means
Ahmad Ridha, Abi Panca
Gumilang
219
38
Temporal Entity Tagging for Indonesian Documents
Ahmad Ridha, Agus Simamora
223
39
Multidimensional Poverty Measurement Using Counting
Approach and Dual Cutoff Method in District of Banyumas
lndah Soraya. lrwan Susanto,
Mania Roswitha
229
vii
40
Minimizing Linear Optimization Model of Basic Reproduc1ion
Number in a Fixed Number of Vaccination Coverage using
Interior Poim Method Approach
0 . Chaerani. A. Anisah. N.
Anggriani, Firdaniza
235
41
Expert System for Plant Gr0\\1h using Hormones and Exogenous
Factors based on Fuzzy Approach
Yaasiin1a Cariens. Karlina Nisa
241
42
The Effect of Divergent Branches on GPU-Based Parallel Program Hendra Rahmawan, Yudi Sa1ria
Pcrfom1ance
Gondoka1yono
247
43
Ensemble of Extreme Estimates Based on Modified
Champemownc and Generalized Pareto Distributions
Aji Hamim Wigena. Anik
Djuraidah, Muhammad Hafid
253
44
Genetic Algorithms Application for Case Study of
Multi-Criteria Decision Analysis (MCDA}
on the Data Contained Missing Value
Septian Rahardiantoro, Oagus
Sartono. Totong Martono
259
45
An Implementation of Parallel AES Algorithm
for Data Encl') pt ion with GPU
Adit>a Erlangga. Endang
Pumama Giri, Karlisa Priandana
265
46
Constructing Orthogonal Fractional Factorial Split-Plot Designs
by Selecting a Subdesign Dependently to Another Subdesign
Bagus Sartono, Yenni Angraini,
lndahwati
269
47
Spatial Clustering of Hotspots using DBSCAN and ST-DBSCAN Utsri Yustina Purwanto, Baba
Barus.and Hari Agung Adrianto
275
48
Gap between the Lower and Upper Bounds for the Iteration
Complexity of Interior-Point Methods
Bib Paruhum Silalahi
281
49
Black Approximation To Determine Value Of Call Option On
Stock In Indonesian Stock Exchange
Jacob Stevy Seleky, Endar H.
Nugrahani. I Gusti Putu Purnaba
287
50
Analysis of Portfolio Optimization With and Without Shortselling Kalecm Saleem, Abdul Kohar
Basd on Diagonal Model : Evidence from Indonesian Stock Market lrwanto, Endar Hasafah
Nugrahani
291
51
Community Network Framework as a Support of Successful
Agricultural Community
Rina Trisminingsih, Christine
Suryadi. Husni S. Sastramihardja
299
52
THE TRANSMISSION MODEL OF DENGUE FEVER
DISEASE: A COMPUTER SIMULA TJON MODEL
Paian Sianturi, Ali Kusnanto,
Fahren Bukhari
305
53
Improving the Independence of the Components ofa
Decomposition in Time Series Data
Hari Wijayanto, Bagus Sartono,
Casia Nursyifa
311
54
Modeling and Empirical Mapping of Vehicular Traffic System:
Case Study of Jabodetabek Region
Endar H. Nugrahani, Hadi
Sumamo, Ali Kusnanto
322
viii
3.,ｾＮ＾＠ ..
D. Biosciences and Bio r eso urces
55
A QuEChERS Based Method for The Detennination of Pesticide
Residues in Indonesian Green Coffee Beans Using Liquid
Chromatography Tandem Mass Spectrometry
Harmoko. Rahmana Emran
Kartasasmita. and Astika
Tresn;m ati
325
56
Design and Implementation of Roaster Control System Using
Image Processing
Mohamad Agung Prawira
Negara, Satryo Budi Utomo.
Sumardi
333
57
Genetic Varia11on of DGA TI Eael Gene of Holstein Friesian m
National Dail)' Cattle Stations
Santiananda A Asmarasari
339
58
The Potency of Dahlia Tubers as Prebiotic for Functional Food
Ainia Herminiati, Sri
Pudjiraharti, Budi Setiawan
345
59
DNA identification using Markov Chain as feature extraction and Toto Haryanto, Habib Rijzaani,
Probabilistic Neural Network as classifier
Muhammad Luthfi Fajar
35 1
60
Multiple Sequence Alignment with Star Method in Graphical
Processing Unit using CU DA
Muhammad Adi Puspo Sujiwo,
Wisnu Ananta Kusuma
359
61
Abalone (Haliotis asinina) Wound Detection System Using
Histogram and Morphology
Noer Fitria Putra Setyono, Aziz
Kustiyo. Dwi Eny Djoko
Setyono
365
62
Local Alignment of DNA Sequence Using Smith-Waterman
Algorithm
Fariz Ashar Himawan,Wisnu
Anania Kusuma
371
63
Agronomic perfonnance and yield potential of 18 com varieties in Anggi Nindita, Willy Bayuardi
Indonesia
Suwarno, Surjono Hadi Sutjahjo.
Perdinan
377
64
Characteristic and Phisychochemical Properties of Sweet Potatoes Ai Mahmudatussa'adah
(Ipomoea batatas L)
381
65
Detennination of Harvesting Time of Three Peanut Varieties
Based on Heat Unit Accumulation
Heni Pumamawati, Yoga
Setiawan Santoso, Yudiwanti
Wahyu
387
66
Respon of Celery (Apium graveolens) Leaves Yield to Plant
Population and Seed Number Per Planting Hole
Karo, B, Marpaung, A. E.,
Tarigan, R., Barus, S. and
Khaririyatun, N .
391
ix
Gap between the Lower and Upper Bounds for the Iteration
Complexity of Interior-Point Methods
Bib Parulwm Silalahi'J
11
Lecturer a1 Depanment of Machemacics. Facult\ of Mathematics and Natural Sciences,
Bogor Agricultural Universicy. Bogor, Indonesia (bibparuhum l@l)ahoo.com)
Abstract
Recenrly, the uu of interior-point methods to solve linear optimi:arion problems, have been becoming great
a/fenrion ro the researchers. The most important thing is that the interior point methods have the best comple..tlf}'
compared to other methods and also efficient in practice Gon:aga. Afomeiro and Adler presented small-update
path-following methods. a varionr of interior-point methods. which is the best known upper bound for the
iteration complexity of an interior-point method. Roos. Terlaky am/ Vial presented an interior-point method
using primal-dual full-Newton step algorithm and state the upper bound fur the iteration complexity of an
interior-point method in difference expression. De:a. Nematollahi. Peyghami and Terlaky showed several worst
cases of the interior-point method by using Klee-Minty problem. Us mg their worst cases. we present a lemma.
where from this lemma we may obtain the lower bound for the iteration complex11y ofan !PM.
KeywQrd:i: interior-point method, upper bound. lower bound
I. INTRODtrCTION
Optimization is the branch of applied
mathematics which studies problems where one
seeks to minimize (or maximize) a real function of
real variables, subject to constraints on the variables.
The solution set of the constraints defines 1he
feasible region (or 1he domain) of an optimization
problem.
II. BRIEF HISTORY Of Ll:'llEAR Ｐｐｔｬｾｚａｉｏｎ＠
Linear Optimization (LO) is concerned with
the minimization or maximization of a linear
function, subject to constraints described by linear
equations and/or linear inequalities.
polynomial number of iterations, and whether there
are linear optimization problems that require an
exponential number of iterations.
The last question was answered by Klee and
Minty (3 ] in 1972. They gave an example of an LO
problem with 2n inequalities for which the simplex
meihod may need as much as Ｒｾ＠ - I iterations.
Their example uses Dantzig's classic most-negativereduce-cost pivot rule.
Then-dimensional Klee-M inty (KM) problem
is given by :
minyn
subject to py._1 ｾＮｖｴ＠
ｾ＠
1- py._ 1, k = l, ... ,n,
A. Simplex Methods
(26)
LO emerged as a mathematical model after
World War II, when Dantzig in 1947 proposed his
simplex method for solving "linear programming"
(then known as optimization) problems [I).
The feasible region of an LO problem is a
polyhedron, the solution set to a system of linear
constraints. Simplex methods move along vertices
of the polyhedron in order to find an optimal vertex.
These methods are designed in such a way that
during this process the value of the objective
function changes monotonically to its optimal value.
After its discovery, the Dantzig simplex
method has inspired much research in mathematics.
Simplex methods were placed as the top I 0
algorithms in the twentieth century by the journal
Computing in Science and Engineering [2]. There
are many variants of a simplex method,
distinguished by rules for selecting the next venex
(so-called pivot rules). The success of simplex
methods have raised some questions such as:
whether there exists a pivot rule that requires a
where p is small positive number by which the unit
Proceedings ISS 2013
=0. The domain is
unit cube in R•. If p =0 then
cube (0, I]" is squashed, and y0
a perturbation of the
the domain is the unit cube and for p e (0, 1/2) it is
a perturbation of the unit cube which is contained in
the unit cube itself, as can easily be verified. Since
the perturbation is small, the domain has the same
number ofvenices as the unit cube, i.e. 2". Klee and
Minty showed that in their example the simplex
method with the Dantzig rule walks along all these
venices. Thus it became clear that the computational
time needed by the Dantzig simplex method may
grow exponentially fast in terms of the number of
inequalities. Since then exponential examples have
been found for almost every pivot rule.
B. The ellipsoid Method
The shortcomings of simplex methods (at least
theoretically) stimulated researchers to look for
other methods with a running time that grows
201
polynomially fast if the number of inequalities
grows. The first polynomial-time algorithm for LO
problems is the ellipsoid method. The basic ideas of
this method evolved from research done in the 1960s
and 1970s in the Soviet Union (as it then was
called). The idea of the ellipsoid method is to
enclose the region of interest by an ellipsoid and to
decrease the volume of the ellipsoid in each iteration
(4]. This method was first published in a paper of
ludin and Nemirovskii [5]. Independently in 1977,
Shor [6) also presented the ellipsoid method.
Khachiyan modified this method and in 1979 (7) he
introduced this method as the first polynomial-time
algorithm for LO problems.
He proved that the ellipsoid method solves an
LO problem in O(n! l) iterations with the total
number of arithmetic operations O(ns l), where n is
the number of inequalities and L is the total bitlength of the input-data. Then in his ｮ･ｾｴ＠
paper (8)
he gave a better bound, 0(11. l) . for the total
number of arithmetic operations.
Following Khachiyan's work, the ellipsoid
method was studied intensively for its theoretical
and practical aspects, with the hope that LO
problems could be solved faster than by simplex
methods. The results were not as expected. In
practice, the rate of convergence of the ellipsoid
method is rather slow. when compared to simplex
methods. The worst-case iteration bound for simplex
methods, in any of its several implementations, is an
extremely poor indicator of the method's actual
perfonnance. On the other hand, the worst-case
bound for the ellipsoid method appears to be a good
indicator for the practical behavior of the ellipsoid
method (9). which makes the method become too
slow for practical purposes.
C. Interior-point Methods
A really effective breakthrough occurred in
1984, when Kannarkar (I OJ proposed a different
polynomial-time method (known as Karmarkar's
projective method) for LO problems. Contrary to
simplex methods, whose iterates are always on the
boundary of the domain,
Kannarkar's method
passes through the interior of the domain to find an
optimal solution.
Jn the worst-case, for a problem with n
inequalities and L bits of input data, his method
requires O(nl) iterations. Jn each iteration,
Karmarkar's paper initiated a revolution in the ,
field of optimization. It gave rise to so-called
interior-point methods (lPMs), fi rst for LO but later
also for the more general class of convex problems.
Renegar. in 1988 ( 11 ). improved the number of
Iterations to 0( f;;L ) iterations. Other variants of
lPMs, called potential reduction methods, require
also only 0( f;;L) iterations. This was shown by Ye
[12). Freund (13), Todd and Ye (14] and Kojima,
Mizuno and Yoshise [ 15]. The main idea of these
methods is the usage of a potential function for
measuring the progress of the method. Kannarkar's
projective method also uses a potential function.
A wide class of IPMs uses the so-called central
path, which was introduced by Sonnevend [ 16) and
Meggido [ 17], as a guide line to the set of optimal
solutions: these methods arc therefore called pathfollowing methods. Small-update path-following
methods, a variant of path-folio\\ ing methods, were
presented Monteiro and Adler [ 18] and Roos and
Vial ( 19). Their methods require 0( f;;L) iterations.
which is the best known upper bound for the
iteration complexity of an IPM . Roos, Terlaky and
Vial in their book (20] obtained the same upper
bound by using an algorithm which is a so-called
primal-dual full-Newton step algorithm. Expressing
the absolute accuracy of the objective function by &
their upper bound for the number of iterations is
rJi; In ｮｾ ｯ＠
(27)
where p 0 > 0 denotes the initial value of the socalled barrier parameter.
Ill. GAP DEnHEN TllE LOWER AND UPPER
BOUNDS
Figure I shows the central path of the 2-dimensional
Klee-Minty (KM) problem for p = l / 3.
,_ .... _
'
·-...._.____---....
--
-------------
Kannarkar's algorithm requires O(nH l) arithmetic
282
--·- ....-....__
Ｍｾ＠
Kannarkar's algorithm requires O(nB) arithmetic
operations and each arithmetic operation needs a
precision of O(l) bits. Jn total, in the worst-case,
operations on numbers with O(l) bits. The
theoretical running time of this algorithm is better
than that of the ellipsoid algorithm by a factor of
0( J; ). More exciting, Kannarkar claimed that the
algorithm is not only efficient in theory, but also in
practice.
l
IU
Figure 1.
M
o.a
---1
-------Q..I
t
y
1
Central path of the 2-dimensional
KM problem, p =11 3.
The central path is an analytic curve that moves
through the interior of the domain to the optimal sel.
Proceedings JSS 2013
Ideally it is a nice smooth curve that goes more or
less straightforward to the optimal set. In that case
path-following methods are extremely efficient. In
practice the curve may possess some sharp turns.
We assume that each such tum will require at least
one iteration of a path-following IPM. As a
consequence we may consider the number of sharp
turns in the central path as a lower bound for the
number of iteration of any path-following IPM.
Recemly, Deza, Nematollahi. Peyghami and
Terlaky [21) showed that when adding abundanily
many suitable chosen redundant constraints to the
KM cube, the squashed cube which is formed by.
the inequalities of KM problem, then one may force
the central path to visit small neighborhoods of all
the vertices of the KM cube.
Deza et al. concluded that an IPM needs at
least 2n - I iterations to solve their problem. Hence
the number of iterations may be exponential in the
dimension n of the cube. This does not contradict
the polynomial-time iteration bound (2) however.
Note that the number of inequalities of the /1 dimensional KM problem is 2n. If N denotes the
number of inequalities in the problem that causes the
central path to visit small neighborhoods of all the
vertices of the KM cube, then the upper bound
should be
o( JN ln(N1-l I e)).
Assuming that
µ 0 I c = 0(1), one may consider this bound as
o( JN In N).
The bound impIies that the number
N of inequalities must be exponential in n as well,
because we should have 2n -I= o(
JN In N).
In [21 ), Deza et al. also argued that such a
redundant KM problem, whose central path visits
small neighborhoods of all the vertices of the KM
cube, gives rise to a lower bound for the maximal
number of iterations in terms of N. Several papers
appeared since then, each new paper using less
redundant constraints and, as a consequence,
yielding a higher lower bound for the iteration
complexity of an IPM. The results of these papers
are summarized in Table I.
Table I. Results from the literature.
Type of
redundant
constraints
Lower
bound for
iteration
complexity
Number
of
redundant
inequalitie
s
PY1-1-Y1 Sd
PY1-1- Y1 S d
PYi-1-Yt Sd
[211
nＨｾＩ＠ ,_._
O(n2'n) .
[22)
In :\'
ｮＨｾＩ＠
O(n'21n)
[23]
n(Ji;)
ｏＨｮＲｾｽ＠
- y 1 Sd1
renc
e
ｮＨｾＩ＠
2°n)
ｏＨｮｾ＠
Refe
.
(24)
In,\'
Column 4 gives the related references. Column I
shows the type of constraints used in the
corresponding paper, column 2 the order of the
number N of inequalities used, and column 3 the
resulting lower bound for the number of iterations of
IPMs. In each case one has N ｾ＠ 2n.
The next lemma explains how the lower
bounds in column 3 can be deduced from the figures
in column 2 of Table I.
Lemma I. If the number N of inequalities
describing a redundant KM problem is O(n1'2"")
and the central path enters a small neighborhood of
each vertex, then any /PM requires at least
ｮＨｾＩ＠
iterations, where
p,q,r > 0.
r
is such that
N ｾｲ｡ｮ､＠
Proof:
It is well known that if an iterate x is on (or close to)
the central path, then the search direction at x in any
interior-point method is (about) tangent to the
central path. The KM path consists of 2" - I line
segments. Since for each sharp tum in the central
path an IPM requires at least one iteration, when
solving the redundant KM problem at least 2n - I
iterations are needed. The number N of inequalities
being O(n"2""), we have N5.cn,.2"' for some
c > 0. This implies
!!..._
< 29" for some
cnP -
c > 0.
Thus we obtain
# iterations +I
Proceedings ISS 2013
ｾ＠
2n
ｾ＠
I
(!!_);;.
cnP
283
From N 2: :r we derive. by raking the 2-logarithm
at both sides. that
log: /\' 2: m.
whence
n ｾ＠ log: N I r . Substituting this we get
J;
7]
I
#
iterations +I 2:
NrP
( c(log? N)"
.
8]
This implies the statement in the lemma.
N o
o
9)
IOJ
JN In__!:!__ =JN In N +JN In!:!_
e
e
= 0( .JN In N).
11]
Comparing this with the highest lower bound in
Table I, which is
n( -/N / In N ). we conclude that
12)
there is still a gap between the lower and upper
bounds for the iteration complexity of IPMs: the
bounds differ by a factor In 2 N.
13]
REFERENCES
IJ
2]
3)
G. 8. Oantzig, linear Programming and
Extensions,
Princeton
N.J. :
Princeton
University Press, 1963.
J. Oongarra and F. Sullivan, "Guest editors :
introduction to the top 10 algorithm,"
Computing in Science and Engineering, vol. 2,
no. I, pp. 22-23, 2000.
V. Klee and G. Minty, "How good is the
simplex algorithm?," in Inequalities, Ill (Proc.
Third Sympos., Univ.California, Los Angeles,
Calif, 1969; dedicated to the memory of
Theodore S. Motzkin, New York, Academic
4]
5)
6]
Press, 1972, pp. 159-175.
D. Luenberger and Y. Ye, linear and
Nonlinear Programming. Third ed. , New York:
Springer, 2008.
0. Iudin and A. Nemirovskii, "Informational
Complexity and Effective Methods of Solution
for Convex Extremal Problems," Ekonomika i
14]
R. Bland, 0 . Goldfarb and M. Todd, "The
Ellipsoid Method: A Survey," Operations
Research. vol. 29, no. 6. pp. 1039- 1091, 1981.
N. Karmarkar. "A new polynomial-time
programming,"
algorithm
for
linear
Combinatorica. vol. 4, no. 4, pp. 373-395,
1984.
J. Renegar, "A polynomial-time algorithm.
based on Newton's method, for linear
programming," Mathematical Programming.
vol. 40. pp. 59-93. 1988.
Y. Ye. "A class of potential functions for Iinear
programming," Iowa City, IA-52242, USA,
1988.
R. Freund, "Polynomial-time algorithms for
linear programming based only on primal
scaling and projected gradients of a potential
function," Mathematical Programming, vol. 51,
pp. 203-222. 1991 .
M. Todd and Y. Ye, "A centered projective
algorithm
for
linear
programming."
Mathematics of Operations Research, vol. 15,
pp. 508-529, 1990.
v/
M. Kojima, S. Mizuno and
A.. "An O(./nl)
15] iteration potential reduction algorithm for linear
complementarity problems." Mathematical
Programming, Series A. vol. 50, pp. 331-342,
1991.
G. Sonnevend, "An analytic center for
16) polyhedrons and new classes of global
algorithms for linear (smooth, convex)
programming," in System Modelling and
Optimization: Proceedings of the 12th IFIPConference held in Budapest, Hungary,
September 1985, Lecture Notes in Control and
Information Sciences ed., vol. 84, Berlin, WestGermany: Springer Verlag, 1986, pp. 866-876.
N. Megiddo, "Pathways to the optimal set in
17) linear programming," in Progress in
Matematicheskie Metody (Translated into
English in Matekon, 13: 25-46, 1977), vol. 12,
Mathematical Programming: Interior Point and
Related Methods, N. Megiddo, Ed., New York,
pp. 357-369, 1976.
N. Shor, "Cut-off Method with Space
Extension in Convex Programming Problems,"
Springer Verlag, 1989, pp. 131--158.
R. Monteiro and L Adler, "Interior-path
I8] following primal-dual algorithms. Part I :
Linear
programming,"
Mathematical
Programming, vol. 44, pp. 27-41 , 1989.
C. Roos and J.-P. Vial, "A polynomial method
19] of approximate centers for linear programming
Kibernetika (Translated into English in
Cybernetics, 13(/):94-96), vol. 13, no. I, pp.
94-95, 1977.
L. Khachiyan, "A Polynomial Algorithm in
284
pp. 1093-1096, 1979.
L. Khachiyan, "Polynomial Algorithms in
Linear Programming," Zhurnal Vychisditel'noi
Alatematilci
Matematicheskot
Fi:ilci
(Translated
into
English
111
USSR
Computational Mathematics and Mathematical
Physics 20:53-72). vol. 20. pp. 51-68. 1980.
o
As staced before, the best known upper bound
for the iteration complexity of an IPM is the bound
in (27). For fixed values of p 0 and & we may \Hite
Linear Programming." Doklady Alwdt!miiu'
Nauk SSSR (Translated into English in So,·iet
Mathematics Dolclady 20, 191--19./). vol. 244,
Proceedings ISS 2013
problem," Mathematica/ Programming, vol. 54.
pp. 295-306, 1992.
Optimi:ation Leuers, vol. 2. no. 3. pp. 403-414.
2008.
C. Roos, T. Terlaky and J.-P. Vial, Interior
B. Jansen, C. Roos and T. Terlaky, "A
25] Polynomial Dikin-type Primal-Dual Algorithm
for Linear Programming," Mmhematics of
Operations Research. vol. 21. pp. 341-353,
1996.
20] Point Methods for Linear Optimization, Second
edition of Theory and Algorithms for Linear
Optimization, Wiley, Chichester. 1997 ed.,
New York: Springer, 2006.
A. Dez.a. E. and Nematollahi, R. Peyghami and
21] T. Terlaky, "The central path visits all 1he
vertices of the Klee-Minty cube," Optimi:ation
Methods & Software. vol. 21. no. 5. pp. 851865, 2006.
A. Dez.a, T. Terlaky and Y. Zinchenko,
path curvature and iterationcomplexity for redundant Klee-Minty cubes."
in Advances in applied mathematics and global
optimi:ation, Adv. Mech. Math. ed., vol. 17,
New York, Springer, 2009, pp. 223--256.
A. Deza, E. Nernatollahi and T. Terlaky, "How
23] good are interior point methods? Klee-Minty
cubes tighten iteration-complexity bounds,"
Alarhematical Programming. vol. 113, no. I,
Ser. A, pp. 1-14, 2008.
E. Nematollahi and T. Terlaky, "A simpler and
24] tighter redundant Klee-Minty construction,"
22] "Central
Proceedings ISS 2013
R. Monteiro, I. Adler and M. Resende, "A
26] polynomial-time primal-dual affine scaling
algorithm for linear and convex quadratic
programming and its power series extension,"
Mathematics of Operations Research. vol. 15,
pp. 191-214, 1990.
T. Tsuchiya, "Affine Scaling Algorithm," in
(27] Interior Point Methods of Mathematical
Programming, T. Terlaky, Ed., Dordrecht, The
Netherlands, Kluwer Academic Publishers,
1996, pp. 35-82.
285
INf; S
P ｬｦＩＨｾｉ＠
Published By
•
.. .. .
'
,..
....
..
I -,
ISBN : 978-979-95093-9-0
PROCEEDINGS
155 2013
International Seminar on Sciences 2013
"Perspectives on Innovative Sciences"
Bogar 15-17 November 2013
IPB International Convention Center
Published by
Faculty of Mathematics and Natural Sciences
Bogar Agricultural University
Copyright© 2014
Faculty of Mathematics and Natural Sciences, Bogor Agricultural University
Proceedings of International Seminar on Sciences 2013 "Perspectives on Innovative Sciences"
Bogor 15-17 November 2013.
Published by: FMIPA-IPB, Jalan Meranti Kampus IPB Dramaga, Bogor 16680
Telp/Fax: 0251 -8625481 /8625708
http://fmipa.ipb.ac.id
ix + 395 pages
ISBN: 978-979-95093-9-0
ii
Boa rd of Editors
PROCEEDINGS
INTERNATIONAL SEMINAR ON SCIENCES 2013
Chief Editor:
Endar H. Nugrahani
Managing Editor:
lndahwati
Nisa Rachmania
Managing Team:
Wisnu Ananta Kusuma
Ali Kusnanto
International Scientific Committee:
Manabu D. Yamanaka (Kobe University, Japan)
Kanaya (Nara Institute of Science and Technology, NAIST, Japan)
Ken Tanaka (Toyama University, Japan)
Daniel Oosgood (Columbia University, USA)
Emmanuel Paradis (lnstitut de Recherche pour le Developpement, IRD, France)
Rizaldi Boer (Begor Agricultural University, Indonesia)
Antonius Suwanto (Begor Agricultural University, Indonesia)
National Reviewer:
Kiagus Dahlan
Tania June
Sri Sugiarti
Miftahudin
Anja Meryandini
Imas Sukaesih Sitanggang
Farit Mochamad Afendi
Paian Sianturi
Husin Alatas
Heru Sukoco
Charlena
Suryani
iii
FOREWORD
The International Seminar on Sciences 2013, which had the main theme "Perspectives on Innovative
Sciences", was organized on November 15 h -1 ih, 2013 by the Faculty of Mathematics and Natural
1
Sciences, Bogor Agricultural University. This event aimed at sharing knowledge and expertise, as well
as building network and collaborations among scientists from various institutions at national and
international level.
Scientific presentations in this seminar consisted of a keynote speech, some invited speeches, and
about 120 contributions of oral and poster presentations. Among the contributions, 66 full papers
have been submitted and reviewed to be published in this proceeding. These papers were clustered in
four groups according to ou r themes:
A. Sustainability and Science Based Agriculture
B. Science of Complexity
C. Mathematics, Statistics and Computer Science
D. Biosciences and Bioresources
In this occasion, we would like to express our thanks and gratitude to our distinguished keynote and
invited speakers: Minister of Science and Technology, Prof. Manabu D. Yamanaka (Kobe University,
Japan), Prof. Kanaya (Nara Institute of Science and Technology, NAIST, Japan), Prof. Ken Tanaka
(Toyama University, Japan), Emmanuel Paradis, PhD. (lnstitut de Recherche pour le Developpement,
IRD, France), Prof. Dr. Ir. Rizaldi Boer, MS (Bogor Agricultural University), and Prof. Dr. Ir. Antonius
Suwanto, M .Sc. (Bogar Agricultural University).
We would like also to extend our thanks and appreciation to all participants and referees for the
wonderful cooperation, the great coordination, and the fascinating efforts. Appreciation and special
thanks are addressed to our colleagues and staffs who help in editing process. Finally, we
acknowledge and express our thanks to all friends, colleagues, and staffs of the Faculty of
Mathematics and Natural Sciences IPB for their help and support.
Bogar, March 2014
The Organizing Committee
International Seminar on Sciences 2013
iv
Table of Content
Page
Board of Editors
Foreword
Table of Content
A. Sustainability and Science Based Agriculture
111
i \I
v
Development of a natural rubber dryer Based on muh1 energy
resources (biomass. solar and wind)
Didin Suwardin, Afrizal
Vachlepi. Mili Pubaya, Sherly
Hanifarianty
3
2
Characterization ofHDTMABr-modified Na1ural Zeolite and its
Application in Cr(VI) Adsorption
Budi Riza Putra. Laiifah K
Darusman, Eti Rohaeti
7
3
Wulan Tri Wahyuni, Latifah K
Potency of Andrographis paniculata, Tinospora crispa, and
Darusman. Rona Jutama
Combination Extract as
a-Glucosidase Inhibitor and Chromatographic Fingerprint Profile
of the Extracts
17
4
Deliana Dahnum, Dyah Styarini,
Utilization of Frond Palm Oil as Second Generation Bioethanol
Production using Alkaline Pretreatment and Separated Hydrolysis Sudiyarmanto, Muryanto.
Haznan Abimanyu
and Fermentation Method
21
5
Pretreatment of Grass Biomass with Biological Process for
Efficient Hydrolysis
6
Alkaloid Compounds from Oil-Free Mahogany Seed (Swietenia Sri Mursiti, Sabirin Matsjeh,
macrophylla, King) and Hypoglycemia Effect of Mahogany Seed Jumina, and Mustafa
on The Rat (Rattus novergicus)
31
7
Utilization Of Vetiver Roots Waste Product as Strong, Low
Density, and Eco Friendly Material Pot
Galuh Suprobo, Tatang
Gunawan, Cynthia Andriani, Rio
Candra lslami
43
8
Green Products from Wastewater of Tempe Industry
Susanti Pudji Hastuti, Yofi
Bramantya Adi, Bary Fratarna.
Samuel Arunglabi,
Dewi KAK Hastuti, and Santoso
Sastrodiharjo
47
9
Saccharification of Oil Palm Empty Fruit Bunch After Alkaline
Pretreatment Followed by Electron Beam Irradiation for Ethanol
Production
Muryanto, Eka Triwahyuni,
Yanni Sudiyani
55
10
Isolation and Screening of Endophytic Bacteria from Bark of Raru Wasinton Simanjuntak, Heri
Plant (Tarrietia ribiginosa) and Their Potential for Bioetahnol
Satria, and Nurul Utami
Production
61
Desy Kumiawati, Muhamad
Natsir, Rahmi Febrialis and
Prima Endang Susilowati
27
v
II
Tht: Effect of Hypenension I lerbs Fonnula to Thi.' Kidne)
Functions
Agus Triyono. Saryanto
67
12
The Use of Activated Carbon from Ointaro Fruit-Shell (Cerbera
manghas) as an Adsorbent to Increase Water Quality
Armi Wulanawati, Kamella
Gustina and Djeni Hendra
71
13
Analysis of Active Compounds from Mangosteen Rind (Garcinia Fachrurrazie, Hall) Noviardi
mangostana L.) by Binding Affinity to The Androgen Receptor as
Anti-Prostate Cancer Drug Candidates
77
14
Antioxidant Activity from Formula of Jati Belanda (Guazuma
S) aefudin. Sulistiyani, Edy
ulmifolia Lamk.), Jambu Biji (Psidium guajava Linn.). and Salam Djauhari Purwakusumah
(Eugenia polyanrha Wight.) Leaves Extract
81
15
Diversity of Bacterial Mercury Reductase Resistance (mer A) from Prima Endang Susilowati, Sapto
Bombana Gold Mine
Raharjo, Rachmawati Rusdin.
Muzuni
87
16
Brake Fem (Pteris vittata) as a Prospective Heavy Metal
Accumulator: Utilization Potentials of Harvested Biomass and
Heavy Metal
Mochamad Taufiq Ridwan. Rike
Tri Kumala Dewi and Agung
I lasan Lukman
91
17
Protein Content Enhancement ofSpirulina platensis by
Phosphorus Limitation and Nitrogen Addition in Beef Carrie
Wastewater Medium
Irving Noor Arifin, lin
Supaninah Noer and Asri Peni
Wulandari
99
18
Development immobilized enzyme of white-rot fungus for
decolorization of RBBR
Ajeng Arum Sari and Sanro
Tachibana
103
19
Simple and Rapid Screening Method for Early Identification of
Salt Tolerant Foxtail Millet (Setaria italica L. Beauv)
Sintho Wahyuning Ardie, Nuru l
Khumaida, and Amin Nur
109
20
Synthesis of Silver Nanoparticles by Using Extracellular
Metabolites of Lactobacillus delbrueckii subsp. bulgaricus
Suryani, Ridho Pratama, Dimas
Andrianto
113
B. Science of Complexity
119
21
Regional Heat Capacity Changes due to Changes of Land Cover
Composition Using Landsat-5 TM Data
Winda Aryani, !dung Risdiyanto
121
22
Microbial Cellulolytic Isolation and Identification from Durian
Leather Waste
Hapsoh, Gusmawartati dan
Ujang Al Husnah
129
23
Predicting Water Surplus and Water Deficit in the Paddy Rice
Production Center in North Sulawesi Using the Water Balance
Model
Johanis H. Panelewen, Johannes
E. X. Rogi and Wiske
Rotinsulu3
135
24
Prediction of Oustfall Generation in Ambient Air over an
lnceptisol Soil Area
Arief Sabdo Yuwono, Lia
Amaliah
143
vi
25
Fitri Adilla, Lisman
Carboxymethyla1ton of Microfibrillated Cellulose to Improve
Thermal and Mechanical Properties of Polylactic Acid Composites Suryanegara. Suminar S.
Achmadi
149
26
Esterification of Microfibrillated Cellulose with Various
Anhydrides to Improve Thermal and Mechanical Properties of
Polylactic Acid Composite
Ajeng Ma\\ angi. Lisman
Suryanegara, Suminar S.
Achmad1
155
27
Thermal and Mechanical Properties Improvement of Pol) lactic
Acid-Nanocellulose Composites by Acetylation
Resty Dwi Andinie, Lisman
Suryanegara. Suminar S.
Achmadi
161
167
C. Mathematics, Sta tistics a nd Computer Science
28
Rado Yendra, Ari Pani Desvina,
The comparison spatial distribution observed. cstimatated using
Neyman-Scon Rectangular Pulse Method (NSRP}, and simulation Abdul Aziz Jemain
for mean of one-hour rain and probability of 24-hour rain
169
29
Optimal VAR Injection Based on Neural Network Current State
Estimator for 20kV Surabaya Electrical Distribution System
Dimas Fajar Uman P, Ontoseno
Penangsang, Adi Soeprijanto
175
30
Fire-Fighting Robot Navigat ion System Using Wall Following
Algorithm and Fuzzy Logic
Karlisa Priandana. Erwin M Y
Chriswantoro, Mushthofa
181
31
Analysis and Solving of Outliers in Longitudinal Data
Viani Eminita, lndahwati.
Anang Kumia
187
32
Implementation of Flowers and Ornamental Plants Landscape
Information System using Cloud Computing Technology
Meuthia Rachmaniah and
lswarawati
193
33
Cluster Information of Non-sampled Area in Small Area
Estimation with Non-normally Distributed Area Random Effects
and Auxiliary Variables
Rahma Anisa, Anang Kumia,
lndahwati
199
34
Study of Overdispersion for Poisson and Zero-Inflated Poisson
Regression on Some Characteristics of the Data
Lili Puspita Rahayu, Kusman
Sadik, lndahwati
203
35
The Effect of Two-Way and Three-Way Interaction of Perceived
Rewards on the Relationship Quality
Enny Kristiani, Ujang
Sumarwan, Lilik Noor Yulianti
& Asep Saefuddin
209
36
Implementation of Inverse Kinematics for the Coordination
Control of Six Legged Robot
Wulandari, Karlisa Priandana,
Agus Buono
213
37
Detection ofC Code Plagiarism by Using K-Means
Ahmad Ridha, Abi Panca
Gumilang
219
38
Temporal Entity Tagging for Indonesian Documents
Ahmad Ridha, Agus Simamora
223
39
Multidimensional Poverty Measurement Using Counting
Approach and Dual Cutoff Method in District of Banyumas
lndah Soraya. lrwan Susanto,
Mania Roswitha
229
vii
40
Minimizing Linear Optimization Model of Basic Reproduc1ion
Number in a Fixed Number of Vaccination Coverage using
Interior Poim Method Approach
0 . Chaerani. A. Anisah. N.
Anggriani, Firdaniza
235
41
Expert System for Plant Gr0\\1h using Hormones and Exogenous
Factors based on Fuzzy Approach
Yaasiin1a Cariens. Karlina Nisa
241
42
The Effect of Divergent Branches on GPU-Based Parallel Program Hendra Rahmawan, Yudi Sa1ria
Pcrfom1ance
Gondoka1yono
247
43
Ensemble of Extreme Estimates Based on Modified
Champemownc and Generalized Pareto Distributions
Aji Hamim Wigena. Anik
Djuraidah, Muhammad Hafid
253
44
Genetic Algorithms Application for Case Study of
Multi-Criteria Decision Analysis (MCDA}
on the Data Contained Missing Value
Septian Rahardiantoro, Oagus
Sartono. Totong Martono
259
45
An Implementation of Parallel AES Algorithm
for Data Encl') pt ion with GPU
Adit>a Erlangga. Endang
Pumama Giri, Karlisa Priandana
265
46
Constructing Orthogonal Fractional Factorial Split-Plot Designs
by Selecting a Subdesign Dependently to Another Subdesign
Bagus Sartono, Yenni Angraini,
lndahwati
269
47
Spatial Clustering of Hotspots using DBSCAN and ST-DBSCAN Utsri Yustina Purwanto, Baba
Barus.and Hari Agung Adrianto
275
48
Gap between the Lower and Upper Bounds for the Iteration
Complexity of Interior-Point Methods
Bib Paruhum Silalahi
281
49
Black Approximation To Determine Value Of Call Option On
Stock In Indonesian Stock Exchange
Jacob Stevy Seleky, Endar H.
Nugrahani. I Gusti Putu Purnaba
287
50
Analysis of Portfolio Optimization With and Without Shortselling Kalecm Saleem, Abdul Kohar
Basd on Diagonal Model : Evidence from Indonesian Stock Market lrwanto, Endar Hasafah
Nugrahani
291
51
Community Network Framework as a Support of Successful
Agricultural Community
Rina Trisminingsih, Christine
Suryadi. Husni S. Sastramihardja
299
52
THE TRANSMISSION MODEL OF DENGUE FEVER
DISEASE: A COMPUTER SIMULA TJON MODEL
Paian Sianturi, Ali Kusnanto,
Fahren Bukhari
305
53
Improving the Independence of the Components ofa
Decomposition in Time Series Data
Hari Wijayanto, Bagus Sartono,
Casia Nursyifa
311
54
Modeling and Empirical Mapping of Vehicular Traffic System:
Case Study of Jabodetabek Region
Endar H. Nugrahani, Hadi
Sumamo, Ali Kusnanto
322
viii
3.,ｾＮ＾＠ ..
D. Biosciences and Bio r eso urces
55
A QuEChERS Based Method for The Detennination of Pesticide
Residues in Indonesian Green Coffee Beans Using Liquid
Chromatography Tandem Mass Spectrometry
Harmoko. Rahmana Emran
Kartasasmita. and Astika
Tresn;m ati
325
56
Design and Implementation of Roaster Control System Using
Image Processing
Mohamad Agung Prawira
Negara, Satryo Budi Utomo.
Sumardi
333
57
Genetic Varia11on of DGA TI Eael Gene of Holstein Friesian m
National Dail)' Cattle Stations
Santiananda A Asmarasari
339
58
The Potency of Dahlia Tubers as Prebiotic for Functional Food
Ainia Herminiati, Sri
Pudjiraharti, Budi Setiawan
345
59
DNA identification using Markov Chain as feature extraction and Toto Haryanto, Habib Rijzaani,
Probabilistic Neural Network as classifier
Muhammad Luthfi Fajar
35 1
60
Multiple Sequence Alignment with Star Method in Graphical
Processing Unit using CU DA
Muhammad Adi Puspo Sujiwo,
Wisnu Ananta Kusuma
359
61
Abalone (Haliotis asinina) Wound Detection System Using
Histogram and Morphology
Noer Fitria Putra Setyono, Aziz
Kustiyo. Dwi Eny Djoko
Setyono
365
62
Local Alignment of DNA Sequence Using Smith-Waterman
Algorithm
Fariz Ashar Himawan,Wisnu
Anania Kusuma
371
63
Agronomic perfonnance and yield potential of 18 com varieties in Anggi Nindita, Willy Bayuardi
Indonesia
Suwarno, Surjono Hadi Sutjahjo.
Perdinan
377
64
Characteristic and Phisychochemical Properties of Sweet Potatoes Ai Mahmudatussa'adah
(Ipomoea batatas L)
381
65
Detennination of Harvesting Time of Three Peanut Varieties
Based on Heat Unit Accumulation
Heni Pumamawati, Yoga
Setiawan Santoso, Yudiwanti
Wahyu
387
66
Respon of Celery (Apium graveolens) Leaves Yield to Plant
Population and Seed Number Per Planting Hole
Karo, B, Marpaung, A. E.,
Tarigan, R., Barus, S. and
Khaririyatun, N .
391
ix
Gap between the Lower and Upper Bounds for the Iteration
Complexity of Interior-Point Methods
Bib Parulwm Silalahi'J
11
Lecturer a1 Depanment of Machemacics. Facult\ of Mathematics and Natural Sciences,
Bogor Agricultural Universicy. Bogor, Indonesia (bibparuhum l@l)ahoo.com)
Abstract
Recenrly, the uu of interior-point methods to solve linear optimi:arion problems, have been becoming great
a/fenrion ro the researchers. The most important thing is that the interior point methods have the best comple..tlf}'
compared to other methods and also efficient in practice Gon:aga. Afomeiro and Adler presented small-update
path-following methods. a varionr of interior-point methods. which is the best known upper bound for the
iteration complexity of an interior-point method. Roos. Terlaky am/ Vial presented an interior-point method
using primal-dual full-Newton step algorithm and state the upper bound fur the iteration complexity of an
interior-point method in difference expression. De:a. Nematollahi. Peyghami and Terlaky showed several worst
cases of the interior-point method by using Klee-Minty problem. Us mg their worst cases. we present a lemma.
where from this lemma we may obtain the lower bound for the iteration complex11y ofan !PM.
KeywQrd:i: interior-point method, upper bound. lower bound
I. INTRODtrCTION
Optimization is the branch of applied
mathematics which studies problems where one
seeks to minimize (or maximize) a real function of
real variables, subject to constraints on the variables.
The solution set of the constraints defines 1he
feasible region (or 1he domain) of an optimization
problem.
II. BRIEF HISTORY Of Ll:'llEAR Ｐｐｔｬｾｚａｉｏｎ＠
Linear Optimization (LO) is concerned with
the minimization or maximization of a linear
function, subject to constraints described by linear
equations and/or linear inequalities.
polynomial number of iterations, and whether there
are linear optimization problems that require an
exponential number of iterations.
The last question was answered by Klee and
Minty (3 ] in 1972. They gave an example of an LO
problem with 2n inequalities for which the simplex
meihod may need as much as Ｒｾ＠ - I iterations.
Their example uses Dantzig's classic most-negativereduce-cost pivot rule.
Then-dimensional Klee-M inty (KM) problem
is given by :
minyn
subject to py._1 ｾＮｖｴ＠
ｾ＠
1- py._ 1, k = l, ... ,n,
A. Simplex Methods
(26)
LO emerged as a mathematical model after
World War II, when Dantzig in 1947 proposed his
simplex method for solving "linear programming"
(then known as optimization) problems [I).
The feasible region of an LO problem is a
polyhedron, the solution set to a system of linear
constraints. Simplex methods move along vertices
of the polyhedron in order to find an optimal vertex.
These methods are designed in such a way that
during this process the value of the objective
function changes monotonically to its optimal value.
After its discovery, the Dantzig simplex
method has inspired much research in mathematics.
Simplex methods were placed as the top I 0
algorithms in the twentieth century by the journal
Computing in Science and Engineering [2]. There
are many variants of a simplex method,
distinguished by rules for selecting the next venex
(so-called pivot rules). The success of simplex
methods have raised some questions such as:
whether there exists a pivot rule that requires a
where p is small positive number by which the unit
Proceedings ISS 2013
=0. The domain is
unit cube in R•. If p =0 then
cube (0, I]" is squashed, and y0
a perturbation of the
the domain is the unit cube and for p e (0, 1/2) it is
a perturbation of the unit cube which is contained in
the unit cube itself, as can easily be verified. Since
the perturbation is small, the domain has the same
number ofvenices as the unit cube, i.e. 2". Klee and
Minty showed that in their example the simplex
method with the Dantzig rule walks along all these
venices. Thus it became clear that the computational
time needed by the Dantzig simplex method may
grow exponentially fast in terms of the number of
inequalities. Since then exponential examples have
been found for almost every pivot rule.
B. The ellipsoid Method
The shortcomings of simplex methods (at least
theoretically) stimulated researchers to look for
other methods with a running time that grows
201
polynomially fast if the number of inequalities
grows. The first polynomial-time algorithm for LO
problems is the ellipsoid method. The basic ideas of
this method evolved from research done in the 1960s
and 1970s in the Soviet Union (as it then was
called). The idea of the ellipsoid method is to
enclose the region of interest by an ellipsoid and to
decrease the volume of the ellipsoid in each iteration
(4]. This method was first published in a paper of
ludin and Nemirovskii [5]. Independently in 1977,
Shor [6) also presented the ellipsoid method.
Khachiyan modified this method and in 1979 (7) he
introduced this method as the first polynomial-time
algorithm for LO problems.
He proved that the ellipsoid method solves an
LO problem in O(n! l) iterations with the total
number of arithmetic operations O(ns l), where n is
the number of inequalities and L is the total bitlength of the input-data. Then in his ｮ･ｾｴ＠
paper (8)
he gave a better bound, 0(11. l) . for the total
number of arithmetic operations.
Following Khachiyan's work, the ellipsoid
method was studied intensively for its theoretical
and practical aspects, with the hope that LO
problems could be solved faster than by simplex
methods. The results were not as expected. In
practice, the rate of convergence of the ellipsoid
method is rather slow. when compared to simplex
methods. The worst-case iteration bound for simplex
methods, in any of its several implementations, is an
extremely poor indicator of the method's actual
perfonnance. On the other hand, the worst-case
bound for the ellipsoid method appears to be a good
indicator for the practical behavior of the ellipsoid
method (9). which makes the method become too
slow for practical purposes.
C. Interior-point Methods
A really effective breakthrough occurred in
1984, when Kannarkar (I OJ proposed a different
polynomial-time method (known as Karmarkar's
projective method) for LO problems. Contrary to
simplex methods, whose iterates are always on the
boundary of the domain,
Kannarkar's method
passes through the interior of the domain to find an
optimal solution.
Jn the worst-case, for a problem with n
inequalities and L bits of input data, his method
requires O(nl) iterations. Jn each iteration,
Karmarkar's paper initiated a revolution in the ,
field of optimization. It gave rise to so-called
interior-point methods (lPMs), fi rst for LO but later
also for the more general class of convex problems.
Renegar. in 1988 ( 11 ). improved the number of
Iterations to 0( f;;L ) iterations. Other variants of
lPMs, called potential reduction methods, require
also only 0( f;;L) iterations. This was shown by Ye
[12). Freund (13), Todd and Ye (14] and Kojima,
Mizuno and Yoshise [ 15]. The main idea of these
methods is the usage of a potential function for
measuring the progress of the method. Kannarkar's
projective method also uses a potential function.
A wide class of IPMs uses the so-called central
path, which was introduced by Sonnevend [ 16) and
Meggido [ 17], as a guide line to the set of optimal
solutions: these methods arc therefore called pathfollowing methods. Small-update path-following
methods, a variant of path-folio\\ ing methods, were
presented Monteiro and Adler [ 18] and Roos and
Vial ( 19). Their methods require 0( f;;L) iterations.
which is the best known upper bound for the
iteration complexity of an IPM . Roos, Terlaky and
Vial in their book (20] obtained the same upper
bound by using an algorithm which is a so-called
primal-dual full-Newton step algorithm. Expressing
the absolute accuracy of the objective function by &
their upper bound for the number of iterations is
rJi; In ｮｾ ｯ＠
(27)
where p 0 > 0 denotes the initial value of the socalled barrier parameter.
Ill. GAP DEnHEN TllE LOWER AND UPPER
BOUNDS
Figure I shows the central path of the 2-dimensional
Klee-Minty (KM) problem for p = l / 3.
,_ .... _
'
·-...._.____---....
--
-------------
Kannarkar's algorithm requires O(nH l) arithmetic
282
--·- ....-....__
Ｍｾ＠
Kannarkar's algorithm requires O(nB) arithmetic
operations and each arithmetic operation needs a
precision of O(l) bits. Jn total, in the worst-case,
operations on numbers with O(l) bits. The
theoretical running time of this algorithm is better
than that of the ellipsoid algorithm by a factor of
0( J; ). More exciting, Kannarkar claimed that the
algorithm is not only efficient in theory, but also in
practice.
l
IU
Figure 1.
M
o.a
---1
-------Q..I
t
y
1
Central path of the 2-dimensional
KM problem, p =11 3.
The central path is an analytic curve that moves
through the interior of the domain to the optimal sel.
Proceedings JSS 2013
Ideally it is a nice smooth curve that goes more or
less straightforward to the optimal set. In that case
path-following methods are extremely efficient. In
practice the curve may possess some sharp turns.
We assume that each such tum will require at least
one iteration of a path-following IPM. As a
consequence we may consider the number of sharp
turns in the central path as a lower bound for the
number of iteration of any path-following IPM.
Recemly, Deza, Nematollahi. Peyghami and
Terlaky [21) showed that when adding abundanily
many suitable chosen redundant constraints to the
KM cube, the squashed cube which is formed by.
the inequalities of KM problem, then one may force
the central path to visit small neighborhoods of all
the vertices of the KM cube.
Deza et al. concluded that an IPM needs at
least 2n - I iterations to solve their problem. Hence
the number of iterations may be exponential in the
dimension n of the cube. This does not contradict
the polynomial-time iteration bound (2) however.
Note that the number of inequalities of the /1 dimensional KM problem is 2n. If N denotes the
number of inequalities in the problem that causes the
central path to visit small neighborhoods of all the
vertices of the KM cube, then the upper bound
should be
o( JN ln(N1-l I e)).
Assuming that
µ 0 I c = 0(1), one may consider this bound as
o( JN In N).
The bound impIies that the number
N of inequalities must be exponential in n as well,
because we should have 2n -I= o(
JN In N).
In [21 ), Deza et al. also argued that such a
redundant KM problem, whose central path visits
small neighborhoods of all the vertices of the KM
cube, gives rise to a lower bound for the maximal
number of iterations in terms of N. Several papers
appeared since then, each new paper using less
redundant constraints and, as a consequence,
yielding a higher lower bound for the iteration
complexity of an IPM. The results of these papers
are summarized in Table I.
Table I. Results from the literature.
Type of
redundant
constraints
Lower
bound for
iteration
complexity
Number
of
redundant
inequalitie
s
PY1-1-Y1 Sd
PY1-1- Y1 S d
PYi-1-Yt Sd
[211
nＨｾＩ＠ ,_._
O(n2'n) .
[22)
In :\'
ｮＨｾＩ＠
O(n'21n)
[23]
n(Ji;)
ｏＨｮＲｾｽ＠
- y 1 Sd1
renc
e
ｮＨｾＩ＠
2°n)
ｏＨｮｾ＠
Refe
.
(24)
In,\'
Column 4 gives the related references. Column I
shows the type of constraints used in the
corresponding paper, column 2 the order of the
number N of inequalities used, and column 3 the
resulting lower bound for the number of iterations of
IPMs. In each case one has N ｾ＠ 2n.
The next lemma explains how the lower
bounds in column 3 can be deduced from the figures
in column 2 of Table I.
Lemma I. If the number N of inequalities
describing a redundant KM problem is O(n1'2"")
and the central path enters a small neighborhood of
each vertex, then any /PM requires at least
ｮＨｾＩ＠
iterations, where
p,q,r > 0.
r
is such that
N ｾｲ｡ｮ､＠
Proof:
It is well known that if an iterate x is on (or close to)
the central path, then the search direction at x in any
interior-point method is (about) tangent to the
central path. The KM path consists of 2" - I line
segments. Since for each sharp tum in the central
path an IPM requires at least one iteration, when
solving the redundant KM problem at least 2n - I
iterations are needed. The number N of inequalities
being O(n"2""), we have N5.cn,.2"' for some
c > 0. This implies
!!..._
< 29" for some
cnP -
c > 0.
Thus we obtain
# iterations +I
Proceedings ISS 2013
ｾ＠
2n
ｾ＠
I
(!!_);;.
cnP
283
From N 2: :r we derive. by raking the 2-logarithm
at both sides. that
log: /\' 2: m.
whence
n ｾ＠ log: N I r . Substituting this we get
J;
7]
I
#
iterations +I 2:
NrP
( c(log? N)"
.
8]
This implies the statement in the lemma.
N o
o
9)
IOJ
JN In__!:!__ =JN In N +JN In!:!_
e
e
= 0( .JN In N).
11]
Comparing this with the highest lower bound in
Table I, which is
n( -/N / In N ). we conclude that
12)
there is still a gap between the lower and upper
bounds for the iteration complexity of IPMs: the
bounds differ by a factor In 2 N.
13]
REFERENCES
IJ
2]
3)
G. 8. Oantzig, linear Programming and
Extensions,
Princeton
N.J. :
Princeton
University Press, 1963.
J. Oongarra and F. Sullivan, "Guest editors :
introduction to the top 10 algorithm,"
Computing in Science and Engineering, vol. 2,
no. I, pp. 22-23, 2000.
V. Klee and G. Minty, "How good is the
simplex algorithm?," in Inequalities, Ill (Proc.
Third Sympos., Univ.California, Los Angeles,
Calif, 1969; dedicated to the memory of
Theodore S. Motzkin, New York, Academic
4]
5)
6]
Press, 1972, pp. 159-175.
D. Luenberger and Y. Ye, linear and
Nonlinear Programming. Third ed. , New York:
Springer, 2008.
0. Iudin and A. Nemirovskii, "Informational
Complexity and Effective Methods of Solution
for Convex Extremal Problems," Ekonomika i
14]
R. Bland, 0 . Goldfarb and M. Todd, "The
Ellipsoid Method: A Survey," Operations
Research. vol. 29, no. 6. pp. 1039- 1091, 1981.
N. Karmarkar. "A new polynomial-time
programming,"
algorithm
for
linear
Combinatorica. vol. 4, no. 4, pp. 373-395,
1984.
J. Renegar, "A polynomial-time algorithm.
based on Newton's method, for linear
programming," Mathematical Programming.
vol. 40. pp. 59-93. 1988.
Y. Ye. "A class of potential functions for Iinear
programming," Iowa City, IA-52242, USA,
1988.
R. Freund, "Polynomial-time algorithms for
linear programming based only on primal
scaling and projected gradients of a potential
function," Mathematical Programming, vol. 51,
pp. 203-222. 1991 .
M. Todd and Y. Ye, "A centered projective
algorithm
for
linear
programming."
Mathematics of Operations Research, vol. 15,
pp. 508-529, 1990.
v/
M. Kojima, S. Mizuno and
A.. "An O(./nl)
15] iteration potential reduction algorithm for linear
complementarity problems." Mathematical
Programming, Series A. vol. 50, pp. 331-342,
1991.
G. Sonnevend, "An analytic center for
16) polyhedrons and new classes of global
algorithms for linear (smooth, convex)
programming," in System Modelling and
Optimization: Proceedings of the 12th IFIPConference held in Budapest, Hungary,
September 1985, Lecture Notes in Control and
Information Sciences ed., vol. 84, Berlin, WestGermany: Springer Verlag, 1986, pp. 866-876.
N. Megiddo, "Pathways to the optimal set in
17) linear programming," in Progress in
Matematicheskie Metody (Translated into
English in Matekon, 13: 25-46, 1977), vol. 12,
Mathematical Programming: Interior Point and
Related Methods, N. Megiddo, Ed., New York,
pp. 357-369, 1976.
N. Shor, "Cut-off Method with Space
Extension in Convex Programming Problems,"
Springer Verlag, 1989, pp. 131--158.
R. Monteiro and L Adler, "Interior-path
I8] following primal-dual algorithms. Part I :
Linear
programming,"
Mathematical
Programming, vol. 44, pp. 27-41 , 1989.
C. Roos and J.-P. Vial, "A polynomial method
19] of approximate centers for linear programming
Kibernetika (Translated into English in
Cybernetics, 13(/):94-96), vol. 13, no. I, pp.
94-95, 1977.
L. Khachiyan, "A Polynomial Algorithm in
284
pp. 1093-1096, 1979.
L. Khachiyan, "Polynomial Algorithms in
Linear Programming," Zhurnal Vychisditel'noi
Alatematilci
Matematicheskot
Fi:ilci
(Translated
into
English
111
USSR
Computational Mathematics and Mathematical
Physics 20:53-72). vol. 20. pp. 51-68. 1980.
o
As staced before, the best known upper bound
for the iteration complexity of an IPM is the bound
in (27). For fixed values of p 0 and & we may \Hite
Linear Programming." Doklady Alwdt!miiu'
Nauk SSSR (Translated into English in So,·iet
Mathematics Dolclady 20, 191--19./). vol. 244,
Proceedings ISS 2013
problem," Mathematica/ Programming, vol. 54.
pp. 295-306, 1992.
Optimi:ation Leuers, vol. 2. no. 3. pp. 403-414.
2008.
C. Roos, T. Terlaky and J.-P. Vial, Interior
B. Jansen, C. Roos and T. Terlaky, "A
25] Polynomial Dikin-type Primal-Dual Algorithm
for Linear Programming," Mmhematics of
Operations Research. vol. 21. pp. 341-353,
1996.
20] Point Methods for Linear Optimization, Second
edition of Theory and Algorithms for Linear
Optimization, Wiley, Chichester. 1997 ed.,
New York: Springer, 2006.
A. Dez.a. E. and Nematollahi, R. Peyghami and
21] T. Terlaky, "The central path visits all 1he
vertices of the Klee-Minty cube," Optimi:ation
Methods & Software. vol. 21. no. 5. pp. 851865, 2006.
A. Dez.a, T. Terlaky and Y. Zinchenko,
path curvature and iterationcomplexity for redundant Klee-Minty cubes."
in Advances in applied mathematics and global
optimi:ation, Adv. Mech. Math. ed., vol. 17,
New York, Springer, 2009, pp. 223--256.
A. Deza, E. Nernatollahi and T. Terlaky, "How
23] good are interior point methods? Klee-Minty
cubes tighten iteration-complexity bounds,"
Alarhematical Programming. vol. 113, no. I,
Ser. A, pp. 1-14, 2008.
E. Nematollahi and T. Terlaky, "A simpler and
24] tighter redundant Klee-Minty construction,"
22] "Central
Proceedings ISS 2013
R. Monteiro, I. Adler and M. Resende, "A
26] polynomial-time primal-dual affine scaling
algorithm for linear and convex quadratic
programming and its power series extension,"
Mathematics of Operations Research. vol. 15,
pp. 191-214, 1990.
T. Tsuchiya, "Affine Scaling Algorithm," in
(27] Interior Point Methods of Mathematical
Programming, T. Terlaky, Ed., Dordrecht, The
Netherlands, Kluwer Academic Publishers,
1996, pp. 35-82.
285