A Norm Minimization-Based Convex Vector Optimization Algorithm

Date
2022-06-04
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Source Title
Journal of Optimization Theory and Applications
Print ISSN
0022-3239
Electronic ISSN
1573-2878
Publisher
Springer New York LLC
Volume
194
Issue
2
Pages
681 - 712
Language
English
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Abstract

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations. Unlike Pascoletti–Serafini scalarization used in the literature for similar purposes, it does not involve a direction parameter. Therefore, the algorithm is free of direction-biasedness. We also propose a modification of the algorithm by introducing a suitable compact subset of the upper image, which helps in proving for the first time the finiteness of an algorithm for convex vector optimization. The computational performance of the algorithms is illustrated using some of the benchmark test problems, which shows promising results in comparison to a similar algorithm that is based on Pascoletti–Serafini scalarization.

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Published Version (Please cite this version)