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

2023/05/24 by Andreas Löhne, Löhne, Andreas
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2305.15575

openalex publication_date 2023/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 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.

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