Existence of solutions for polyhedral convex set optimization problems

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear programs and multiple objective linear programs provide proper subc...

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Veröffentlicht in:	Optimization Jg. 73; H. 11; S. 3339 - 3349
1. Verfasser:	Löhne, Andreas
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Philadelphia Taylor & Francis 01.11.2024 Taylor & Francis LLC
Schlagworte:	Convexity Linear programming Multiple objective analysis multiple objective linear programming Optimization Set optimization vector linear programming
ISSN:	0233-1934, 1029-4945
Online-Zugang:	Volltext
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Zusammenfassung:	Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear programs and multiple objective linear programs provide proper subclasses. In this article, we choose a solution concept for arbitrary polyhedral convex set optimization problems out of several alternatives, show existence of solutions and characterize the existence of solutions in different ways. Two known results are obtained as particular cases, both with proofs being easier than the original ones: The existence of solutions of bounded polyhedral convex set optimization problems and a characterization of the existence of solutions of vector linear programs.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0233-1934 1029-4945
DOI:	10.1080/02331934.2023.2280018