Geometric duality results and approximation algorithms for convex vector optimization problems

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buir.contributor.authorArarat, Çağın
buir.contributor.authorUlus, Firdevs
buir.contributor.orcidArarat, Çağın|0000-0002-6985-7665
buir.contributor.orcidUlus, Firdevs|0000-0002-0532-9927
dc.citation.epage146en_US
dc.citation.issueNumber1
dc.citation.spage116
dc.citation.volumeNumber33
dc.contributor.authorArarat, Çağın
dc.contributor.authorTekgül, S.
dc.contributor.authorUlus, Firdevs
dc.date.accessioned2024-03-08T19:31:06Z
dc.date.available2024-03-08T19:31:06Z
dc.date.issued2023-01-27
dc.departmentDepartment of Industrial Engineering
dc.description.abstractWe study geometric duality for convex vector optimization problems. For a primal problem with a q-dimensional objective space, we formulate a dual problem with a (q+1)-dimensional objective space. Consequently, different from an existing approach, the geometric dual problem does not depend on a fixed direction parameter, and the resulting dual image is a convex cone. We prove a one-to-one correspondence between certain faces of the primal and dual images. In addition, we show that a polyhedral approximation for one image gives rise to a polyhedral approximation for the other. Based on this, we propose a geometric dual algorithm which solves the primal and dual problems simultaneously and is free of direction-biasedness. We also modify an existing direction-free primal algorithm in such a way that it solves the dual problem as well. We test the performance of the algorithms for randomly generated problem instances by using the so-called primal error and hypervolume indicator as performance measures. © 2023 Society for Industrial and Applied Mathematics.
dc.identifier.doi10.1137/21M1458788
dc.identifier.eissn1095-7189
dc.identifier.issn1052-6234
dc.identifier.urihttps://hdl.handle.net/11693/114434
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics Publications
dc.relation.isversionofhttps://doi.org/10.1137/21M1458788
dc.rights.licenseCC BY
dc.source.titleSIAM Journal on Optimization
dc.subjectConvex vector optimization
dc.subjectMultiobjective optimization
dc.subjectApproximation algorithm
dc.subjectScalarization
dc.subjectGeometric duality
dc.subjectHypervolume indicator
dc.titleGeometric duality results and approximation algorithms for convex vector optimization problems
dc.typeArticle

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