Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints

We propose a method for finding a global optimal solution of programs with linear complementarity constraints. This problem arises for instance in bilevel programming. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of...

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Published in:Journal of optimization theory and applications Vol. 124; no. 2; pp. 467 - 490
Main Authors: Thoai, N. V., Yamamoto, Y., Yoshise, A.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.02.2005
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Polytopes
equilibrium constraints
Branch and bound method
Optimization method
Global optimum
Linear programming
Bilevel programming
Programs with linear complementarity constraints
Numerical method
Complementarity problem
Equilibrium condition
Global solution
global optimization
Optimal solution
Mathematical programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Abstract We propose a method for finding a global optimal solution of programs with linear complementarity constraints. This problem arises for instance in bilevel programming. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of iterations or converging to a global optimal solution. The construction of such sequence is based on branch-and-bound techniques, which have been used successfully in global optimization. Results on a numerical test of the algorithm are reported.
AbstractList We propose a method for finding a global optimal solution of programs with linear complementarity constraints. This problem arises for instance in bilevel programming. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite number of iterations or converging to a global optimal solution. The construction of such sequence is based on branch-and-bound techniques, which have been used successfully in global optimization. Results on a numerical test of the algorithm are reported.
Author Yoshise, A.
Yamamoto, Y.
Thoai, N. V.
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CitedBy_id crossref_primary_10_1080_02522667_2010_10700008
crossref_primary_10_1016_j_neucom_2020_04_013
crossref_primary_10_1007_s12667_021_00496_y
crossref_primary_10_1016_j_trc_2021_103002
Cites_doi 10.1007/3-540-54509-3
10.1007/BF01580720
10.1023/A:1011226232107
10.1007/BF02592205
10.1007/978-1-4615-6305-1
10.1016/0305-0548(82)90007-7
10.1287/moor.5.4.556
10.1023/A:1018359900133
10.1017/CBO9780511983658
10.1080/1055678031000120191
10.1007/978-1-4615-0015-5
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Keywords equilibrium constraints
Branch and bound method
Optimization method
Global optimum
Linear programming
Bilevel programming
Programs with linear complementarity constraints
Numerical method
Complementarity problem
Equilibrium condition
Global solution
global optimization
Optimal solution
Mathematical programming
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R. Horst (CR10) 2000
M. Fukushima (CR2) 1998; 10
J. Gotoh (CR8) 2003; 18
K. Shimizu (CR14) 1997
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R. W. Cottle (CR6) 1992
M. Kojima (CR7) 1991
J. F. Bard (CR12) 1982; 9
Z. Q. Luo (CR1) 1996
J. Z. Zhang (CR3) 2001; 19
N. V. Thoai (CR4) 1987
Z. Q. Luo (CR11) 1996; 75
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SubjectTerms Algorithms
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Polytopes
Title Global Optimization Method for Solving Mathematical Programs with Linear Complementarity Constraints
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