Geometric duality results and approximation algorithms for convex vector optimization problems
buir.contributor.author | Ararat, Çağın | |
buir.contributor.author | Ulus, Firdevs | |
buir.contributor.orcid | Ararat, Çağın|0000-0002-6985-7665 | |
buir.contributor.orcid | Ulus, Firdevs|0000-0002-0532-9927 | |
dc.citation.epage | 146 | en_US |
dc.citation.issueNumber | 1 | |
dc.citation.spage | 116 | |
dc.citation.volumeNumber | 33 | |
dc.contributor.author | Ararat, Çağın | |
dc.contributor.author | Tekgül, S. | |
dc.contributor.author | Ulus, Firdevs | |
dc.date.accessioned | 2024-03-08T19:31:06Z | |
dc.date.available | 2024-03-08T19:31:06Z | |
dc.date.issued | 2023-01-27 | |
dc.department | Department of Industrial Engineering | |
dc.description.abstract | We 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.description.provenance | Made available in DSpace on 2024-03-08T19:31:06Z (GMT). No. of bitstreams: 1 GEOMETRIC_DUALITY_RESULTS_AND_APPROXIMATION_ALGORITHMS_FOR_CONVEX_VECTOR_OPTIMIZATION_PROBLEMS.pdf: 1324358 bytes, checksum: c9d1bcff1e7ebba351dab9ad9c7c8c79 (MD5) Previous issue date: 2023-01-27 | en |
dc.identifier.doi | 10.1137/21M1458788 | |
dc.identifier.eissn | 1095-7189 | |
dc.identifier.issn | 1052-6234 | |
dc.identifier.uri | https://hdl.handle.net/11693/114434 | |
dc.language.iso | en | |
dc.publisher | Society for Industrial and Applied Mathematics Publications | |
dc.relation.isversionof | https://doi.org/10.1137/21M1458788 | |
dc.rights.license | CC BY | |
dc.source.title | SIAM Journal on Optimization | |
dc.subject | Convex vector optimization | |
dc.subject | Multiobjective optimization | |
dc.subject | Approximation algorithm | |
dc.subject | Scalarization | |
dc.subject | Geometric duality | |
dc.subject | Hypervolume indicator | |
dc.title | Geometric duality results and approximation algorithms for convex vector optimization problems | |
dc.type | Article |
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