An Inner Approximation Method for Optimization over the Weakly Efficient Set |
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Authors: | Syuuji Yamada Tetsuzo Tanino Masahiro Inuiguchi |
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Institution: | (1) Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka, 565-0871, Japan;(2) Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, Osaka, 565-0871, Japan |
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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. |
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Keywords: | Weakly Efficient Set Global Optimization Dual Problem Inner Approximation Method |
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