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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Vydáno v:Optimization Ročník 73; číslo 12; s. 3653 - 3665
Hlavní autor: Löhne, Andreas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis 01.12.2024
Taylor & Francis LLC
Témata:
Convexity
Mapping
multiple objective linear programming
Optimization
Set optimization
vector linear programming
ISSN:0233-1934, 1029-4945
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2377237