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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Acknowledgements
We are grateful to the anonymous referees for insightful comments allowed us to correct some inaccuracies appearing in the preceding version and for numerous suggestions that improved the presentation. We would also like to thank Prof. Alberto Zaffaroni for his constructive discussion during the revision process.
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Ulus, F. Tractability of convex vector optimization problems in the sense of polyhedral approximations. J Glob Optim 72, 731–742 (2018). https://doi.org/10.1007/s10898-018-0666-6
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DOI: https://doi.org/10.1007/s10898-018-0666-6