Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations
Optimization and Control
2019-05-28 v3
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.
Keywords
Cite
@article{arxiv.1702.05645,
title = {Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations},
author = {Firdevs Ulus},
journal= {arXiv preprint arXiv:1702.05645},
year = {2019}
}