An Inner Approximation Method for Optimization over the Weakly Efficient Set

Authors:
Syuuji Yamada;Tetsuzo Tanino;Masahiro Inuiguchi
Affiliations:
Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan (e-mail: yamada@eie.eng.osaka-u.ac.jp;Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan;Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan
Venue:
Journal of Global Optimization
Year:
2000

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Abstract

In this paper, we consider an optimization problem which aims to minimize a convex function over the weakly efficient set of a multiobjective programming problem. To solve such a problem, we propose an inner approximation algorithm, in which two kinds of convex subproblems are solved successively. These convex subproblems are fairly easy to solve and therefore the proposed algorithm is practically useful. The algorithm always terminates after finitely many iterations by compromising the weak efficiency to a multiobjective programming problem. Moreover, for a subproblem which is solved at each iteration of the algorithm, we suggest a procedure for eliminating redundant constraints.