Algorithms to solve unbounded convex vector optimization problems

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buir.contributor.authorUlus, Firdevs
buir.contributor.orcidUlus, Firdevs|0000-0002-0532-9927
dc.citation.epage2624en_US
dc.citation.issueNumber4
dc.citation.spage2598
dc.citation.volumeNumber33
dc.contributor.authorWagner, A.
dc.contributor.authorUlus, Firdevs
dc.contributor.authorRudloff, B.
dc.contributor.authorKováčová, G.
dc.contributor.authorHey, N.
dc.date.accessioned2024-03-08T19:46:03Z
dc.date.available2024-03-08T19:46:03Z
dc.date.issued2023-10-12
dc.departmentDepartment of Industrial Engineering
dc.description.abstractThis paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [\c C. Ararat, F. Ulus, and M. Umer, J. Optim. Theory Appl., 194 (2022), pp. 681-712], [D. Dörfler, A. Löhne, C. Schneider, and B. Weißing, Optim. Methods Softw., 37 (2022), pp. 1006-1026], [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713-736]. They provide a polyhedral inner and outer approximation of the upper image that have a Hausdorff distance of at most ε. However, it is well known (see [F. Ulus, J. Global Optim., 72 (2018), pp. 731-742]), that for some unbounded problems such polyhedral approximations do not exist. In this paper, we will propose a generalized solution concept, called an (ε,δ)-solution, that allows one to also consider unbounded CVOPs. It is based on additionally bounding the recession cones of the inner and outer polyhedral approximations of the upper image in a meaningful way. An algorithm is proposed that computes such δ-outer and δ-inner approximations of the recession cone of the upper image. In combination with the results of [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713-736] this provides a primal and a dual algorithm that allow one to compute (ε,δ)-solutions of (potentially unbounded) CVOPs. Numerical examples are provided.
dc.description.provenanceMade available in DSpace on 2024-03-08T19:46:03Z (GMT). No. of bitstreams: 1 ALGORITHMS_TO_SOLVE_UNBOUNDED_CONVEX_VECTOR_OPTIMIZATION_PROBLEMS.pdf: 927410 bytes, checksum: 89e710e4efb79d97154d42612bacca1b (MD5) Previous issue date: 2023-10-12en
dc.identifier.doi10.1137/22M1507693
dc.identifier.eissn1095-7189
dc.identifier.issn1052-6234
dc.identifier.urihttps://hdl.handle.net/11693/114435
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematics Publications
dc.relation.isversionofhttps://doi.org/10.1137/22M1507693
dc.rightsCC BY 4.0 DEED (Attribution 4.0 International)
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.source.titleSIAM Journal on Optimization
dc.subjectConvex vector optimization
dc.subjectUnbounded problems
dc.subjectApproximation algorithm
dc.subjectApproximation of cones
dc.titleAlgorithms to solve unbounded convex vector optimization problems
dc.typeArticle

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