Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations

Firdevs Ulus

doi:10.1007/s10898-018-0666-6

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arXiv · 1702.05645

Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations

Firdevs Ulus

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Abstract

There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner and outer approximations to the Pareto frontier. A CVOP with compact feasible region is known to be bounded and there exists a solution of this sense to it. However, it is not known if it is possible to generate polyhedral inner and outer approximations to the Pareto frontier of a CVOP if the feasible region is not compact. This study shows that not all CVOPs are tractable in that sense and gives a characterization of tractable problems in terms of the well known weighted sum scalarization problems.

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BibTeX RIS

Firdevs Ulus. 2018-05-16. Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations. https://doi.org/10.1007/s10898-018-0666-6

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