A Benson-type algorithm for bounded convex vector optimization problems with vertex selection. (4th May 2022)

• Record Type: Journal Article
• Authors: Dörfler, Daniel; Löhne, Andreas; Schneider, Christopher; Weißing, Benjamin
• Is Part Of: Optimization methods and software. Volume 37:Number 3(2022)
• Page Start: 1006
• Page End: 1026
• Publication Date: 2022-05-04
• Subjects: Vector optimization -- multiple objective optimization -- polyhedral approximation -- convex programming -- algorithms; 90C29 -- 90C25 -- 90-08 -- 90C59; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1880579
• Languages: English
• ISSNs: 1055-6788

Abstract

ABSTRACT: We present an algorithm for approximately solving bounded convex vector optimization problems. The algorithm provides both an outer and an inner polyhedral approximation of the upper image. It is a modification of the primal algorithm presented by Löhne, Rudloff, and Ulus in 2014. There, vertices of an already known outer approximation are successively cutoff to improve the approximation error. We propose a new and efficient selection rule for deciding which vertex to cutoff. Numerical examples are provided which illustrate that this method may solve fewer scalar problems overall and therefore may be faster while achieving the same approximation quality.