A solution method for arbitrary polyhedral convex set optimization problems

2023/10/10 by Löhne, Andreas · 2 citations
#90C05 #90C29 #90C99 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2310.06602

Abstract

We provide a solution method for the polyhedral convex set optimization problem, that is, the problem to minimize a set-valued mapping with polyhedral convex graph with respect to a set ordering relation which is generated by a polyhedral convex cone . The method is proven to be correct and finite without any further assumption to the problem.

Cited by

• Nonmonotone Trust-Region Methods for Optimization of Set-Valued Mapping of Finite Cardinality
• Trust-Region Method for Optimization of Set-Valued Maps Given by Finitely Many Functions

Related

• The natural ordering cone of a polyhedral convex set-valued objective mapping
• On unbounded polyhedral convex set optimization problems
• A Decision-Making Method in Polyhedral Convex Set Optimization
• Solving polyhedral d.c. optimization problems via concave minimization
• Relationships between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets