An inner approximation method incorporating with a penalty function method for a reverse convex programming problem

In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set which is defined by the complement of the interior of a compact convex set X. When X is not necessarily a polytope, an inner approximation method has been proposed (J. Optim. Theory A...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 146; no. 1; pp. 57 - 75
Main Authors: Yamada, Syuuji, Tanino, Tetsuzo, Inuiguchi, Masahiro
Format: Journal Article Conference Proceeding
Language:English
Published: Amsterdam Elsevier B.V 01.09.2002
Elsevier
Subjects:
Applied sciences
Dual problem
Exact sciences and technology
Global optimization
Inner approximation method
Mathematical programming
Operational research and scientific management
Operational research. Management science
Penalty function method
Reverse convex programming problem
Inner approximation method
Dual problem
Penalty function method
Global optimization
Reverse convex programming problem
Polytope
Penalty function
Optimal solution
Global optimum
Duality
Convex function
Convex programming
Convergence
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set which is defined by the complement of the interior of a compact convex set X. When X is not necessarily a polytope, an inner approximation method has been proposed (J. Optim. Theory Appl. 107(2) (2000) 357). The algorithm utilizes inner approximation of X by a sequence of polytopes to generate relaxed problems. Then, every accumulation point of the sequence of optimal solutions of relaxed problems is an optimal solution of the original problem. In this paper, we improve the proposed algorithm. By underestimating the optimal value of the relaxed problem, the improved algorithms have the global convergence.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00418-1