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math.OC2023
A solution method for arbitrary polyhedral convex set optimization problems
Andreas Löhne
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…
math.OC2023
The natural ordering cone of a polyhedral convex set-valued objective mapping
Andreas Löhne
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 behavior of a polyhedral conv…
math.OC2023★ 3 cited
Existence of solutions for polyhedral convex set optimization problems
Andreas Löhne
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 l…