Tractability of convex vector optimization problems in the sense of polyhedral approximations
Date
2018
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Source Title
Journal of Global Optimization
Print ISSN
0925-5001
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Springer New York LLC
Volume
72
Issue
4
Pages
731 - 742
Language
English
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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.