A solution method for arbitrary polyhedral convex set optimization problems

TL;DR

This paper introduces a novel, correct, and finite solution method for arbitrary polyhedral convex set optimization problems, which involve minimizing set-valued mappings with polyhedral convex graphs under set orderings.

Contribution

It presents a new, assumption-free algorithm for solving polyhedral convex set optimization problems, expanding the scope of existing methods.

Findings

The method is proven to be correct.

The method terminates finitely.

Applicable to arbitrary polyhedral convex set optimization problems.

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.