Polinomial Kombinatorik
DAFTAR PUSTAKA
Allgower, E.L and Georg, K. (1990). Computational Solution of Nonlinear Systems
of Equations, American Mathematical Society.
Alon, N. and Tarsi M. (1992). Colorings and orientations of graph, Combinatorica,
12, 125-134.
Alon, N. (1999). Combinatorial Nullstellensatz, Combin. Prob. And Comput, 8,
7-29
Bazarra, M, Sharli H. dan Shetty, C. (1993) NonLinear Programming Theory and
Algoritm, 2nd ed, Wiley, New York,
Benhard, Korte. (2006). Combinatorial Optimization, Springer-Verlag
Bernhard Kortes and Vygen J, (2002) Combinatorial Optimizations, volume 21
dari Algorithm and combinatorial Springer Verlag, Berlin edisi kedua.
Chao, C. Y. and Z.Chen. (1993). On Uniquely 3-colorable graphs, Discrete Mathematics, 112, 374-383.
Cottle, R.W, Pang, J.S and Stone, R.E. (1994). The Linear Complementarity Problem., Academic Press, Inc. 30(9).
Cox, J. Little and Shea D. O. (1992). Ideals, Varieties and algorithms. Dickenstein, A. and Emiris, I. (2005), Solving Polynomial Equations: Foundations,
Algorithm and Application, vol. 14 of Algorithm and Comp in mathematics,
Springer-Verlag Heidelberg
Dennis, J.E., Jr. and Schnabel, R.B, (1983). Numerical Methods for Unconstrained
Optimization and Nonlinear Equations. Prentice Hall, Englewood Cliffs, NJ.
Dennis M and Robert W. (2005). Polyhedra related to integer-convex polynomial
systems, Springer-Verlag, 2. 215-231.
Dorit S.Hochbaum and Ari Segev (1989). Analysis of a flow problem with fixed
charge Network, 19(3) : 291-312.
Dantzig. G.B. (1963) Linear programming and extensions. Princeton University
Press, NJ.
Fletcher R (1972). Minimizing general functions subject to linear constraints, in:
F.A. Lootsma, ed. Numerical methods for nonlinear optimization (Academic
Press, London and New York). pp. 279-296.
Gangadwala, J. (2005). Optimal process design for The synthesis of 2,3dimethylbutene-1. Manuscript. Gill P.E. and Murray W.. Quasi-Newton
methods for unconstrained optimization. Journal of Institute of Mathematics
and its Applications 9 (1972) 91-108.
Gill P.E. and Murray W. Quasi-Newton methods for linearly constrained optimization. Report NAC 32 (1973), National Physical Laboratory, Teddington.
Hajiaghayi M.T. Mahdian M.,and .Mirrogni V.S, (2003). The Facility Location
Problem with general cost function. Networks. 42(1) : (42-47).
63
64
Kamesmunagala (2003). Approximation Algorithm for concave cost network Problem. Phd thesis, Stanford University Department of computer science.
Kojima, M. and Shindo, S. ( 1986). Extensions of Newton and Quasi Newton
Methods to Systems of PC1 Equations, Journal of the Operations Research
Society of Japan, 29:352-374.
Loera, J. De et al. (2006). Integer Polinomial Optimization in Fix Dimension,
Mathematics of Operations Research, 31:147-153
Loera, J. De.et al. (2008). Expressing combinatorial Optimization Problem by Systems of Polynomial Equation and nullstellensatz, the journal of combinatoric,
Probability and computing, 20: 1-15.
Loera, J. De.et al. (2010). Computation with combinatorial Polynomial Equation
and inequalities arising in Optimization, the journal of combinatorial Optimization, Probability and computing, 20: 1-20. Lovasz. L (1994). Stable Sets
and polynomials, Discrete Mathematics,124, 137- 153
Lasserre, J.B. (2002). Polynomials nonnegative on a grid and discrete optimization.
Trans. Am. Math. Soc. 354 (2), 631649
More, J.J. 1971. Global Convergence of Newton-Gauss-Seidel Methods. SIAM
Journal on Numerical Analysis 8(2):325-336.
Mangasarian O.L and. Ritter K (1970)., Nonlinear programming, (Academic Press,
New York, pp. 207-243.
Pang, J. S,(1990), Newtons Method for B-Differentiable Equations, Mathematics
of Operations Research, 15:311-341.
Rheinboldt, W.C. 1998. Methods for Solving Systems of Nonlinear Equations, (2nd
Edition). Society for Industrial an d Applied Mathematics.
Shor, N.Z. (1987). Quadratic optimization problems. Izv. Akad. Nauk SSSR Tekhn.
Kibernet. (1), 128 139, 222
Watters, I.J, (1967) Reduction of integer polynomial programming problem to zeroone linear programming problem. Operation Research. 15 171
Allgower, E.L and Georg, K. (1990). Computational Solution of Nonlinear Systems
of Equations, American Mathematical Society.
Alon, N. and Tarsi M. (1992). Colorings and orientations of graph, Combinatorica,
12, 125-134.
Alon, N. (1999). Combinatorial Nullstellensatz, Combin. Prob. And Comput, 8,
7-29
Bazarra, M, Sharli H. dan Shetty, C. (1993) NonLinear Programming Theory and
Algoritm, 2nd ed, Wiley, New York,
Benhard, Korte. (2006). Combinatorial Optimization, Springer-Verlag
Bernhard Kortes and Vygen J, (2002) Combinatorial Optimizations, volume 21
dari Algorithm and combinatorial Springer Verlag, Berlin edisi kedua.
Chao, C. Y. and Z.Chen. (1993). On Uniquely 3-colorable graphs, Discrete Mathematics, 112, 374-383.
Cottle, R.W, Pang, J.S and Stone, R.E. (1994). The Linear Complementarity Problem., Academic Press, Inc. 30(9).
Cox, J. Little and Shea D. O. (1992). Ideals, Varieties and algorithms. Dickenstein, A. and Emiris, I. (2005), Solving Polynomial Equations: Foundations,
Algorithm and Application, vol. 14 of Algorithm and Comp in mathematics,
Springer-Verlag Heidelberg
Dennis, J.E., Jr. and Schnabel, R.B, (1983). Numerical Methods for Unconstrained
Optimization and Nonlinear Equations. Prentice Hall, Englewood Cliffs, NJ.
Dennis M and Robert W. (2005). Polyhedra related to integer-convex polynomial
systems, Springer-Verlag, 2. 215-231.
Dorit S.Hochbaum and Ari Segev (1989). Analysis of a flow problem with fixed
charge Network, 19(3) : 291-312.
Dantzig. G.B. (1963) Linear programming and extensions. Princeton University
Press, NJ.
Fletcher R (1972). Minimizing general functions subject to linear constraints, in:
F.A. Lootsma, ed. Numerical methods for nonlinear optimization (Academic
Press, London and New York). pp. 279-296.
Gangadwala, J. (2005). Optimal process design for The synthesis of 2,3dimethylbutene-1. Manuscript. Gill P.E. and Murray W.. Quasi-Newton
methods for unconstrained optimization. Journal of Institute of Mathematics
and its Applications 9 (1972) 91-108.
Gill P.E. and Murray W. Quasi-Newton methods for linearly constrained optimization. Report NAC 32 (1973), National Physical Laboratory, Teddington.
Hajiaghayi M.T. Mahdian M.,and .Mirrogni V.S, (2003). The Facility Location
Problem with general cost function. Networks. 42(1) : (42-47).
63
64
Kamesmunagala (2003). Approximation Algorithm for concave cost network Problem. Phd thesis, Stanford University Department of computer science.
Kojima, M. and Shindo, S. ( 1986). Extensions of Newton and Quasi Newton
Methods to Systems of PC1 Equations, Journal of the Operations Research
Society of Japan, 29:352-374.
Loera, J. De et al. (2006). Integer Polinomial Optimization in Fix Dimension,
Mathematics of Operations Research, 31:147-153
Loera, J. De.et al. (2008). Expressing combinatorial Optimization Problem by Systems of Polynomial Equation and nullstellensatz, the journal of combinatoric,
Probability and computing, 20: 1-15.
Loera, J. De.et al. (2010). Computation with combinatorial Polynomial Equation
and inequalities arising in Optimization, the journal of combinatorial Optimization, Probability and computing, 20: 1-20. Lovasz. L (1994). Stable Sets
and polynomials, Discrete Mathematics,124, 137- 153
Lasserre, J.B. (2002). Polynomials nonnegative on a grid and discrete optimization.
Trans. Am. Math. Soc. 354 (2), 631649
More, J.J. 1971. Global Convergence of Newton-Gauss-Seidel Methods. SIAM
Journal on Numerical Analysis 8(2):325-336.
Mangasarian O.L and. Ritter K (1970)., Nonlinear programming, (Academic Press,
New York, pp. 207-243.
Pang, J. S,(1990), Newtons Method for B-Differentiable Equations, Mathematics
of Operations Research, 15:311-341.
Rheinboldt, W.C. 1998. Methods for Solving Systems of Nonlinear Equations, (2nd
Edition). Society for Industrial an d Applied Mathematics.
Shor, N.Z. (1987). Quadratic optimization problems. Izv. Akad. Nauk SSSR Tekhn.
Kibernet. (1), 128 139, 222
Watters, I.J, (1967) Reduction of integer polynomial programming problem to zeroone linear programming problem. Operation Research. 15 171