The natural ordering cone of a polyhedral convex set-valued objective mapping

For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behaviour of a polyhedral convex set optimization problem can be characterized by this cone. Under appropriate assumptions, the natural ordering cone...

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Bibliographic Details
Published in:Optimization Vol. 73; no. 12; pp. 3653 - 3665
Main Author: Löhne, Andreas
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 01.12.2024
Taylor & Francis LLC
Subjects:
Convexity
Mapping
multiple objective linear programming
Optimization
Set optimization
vector linear programming
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behaviour of a polyhedral convex set optimization problem can be characterized by this cone. Under appropriate assumptions, the natural ordering cone is proven to be the smallest ordering cone which makes a polyhedral convex set optimization problem solvable.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2377237