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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Published in:Optimization Vol. 73; no. 11; pp. 3339 - 3349
Main Author: Löhne, Andreas
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 01.11.2024
Taylor & Francis LLC
Subjects:
Convexity
Linear programming
Multiple objective analysis
multiple objective linear programming
Optimization
Set optimization
vector linear programming
ISSN:0233-1934, 1029-4945
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Abstract 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.
AbstractList 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.
Author Löhne, Andreas
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Snippet Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is...
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StartPage 3339
SubjectTerms Convexity
Linear programming
Multiple objective analysis
multiple objective linear programming
Optimization
Set optimization
vector linear programming
Title Existence of solutions for polyhedral convex set optimization problems
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