A norm minimization-based convex vector optimization algorithm

TL;DR

This paper introduces a new convex vector optimization algorithm based on norm minimization that generates polyhedral approximations without direction bias, demonstrating promising computational performance on benchmark problems.

Contribution

It presents a novel outer approximation algorithm using norm-minimizing scalarizations that avoids direction bias and proves its finiteness with a modified approach.

Findings

Algorithm effectively approximates the upper image of convex vector problems.

Finiteness of the algorithm is established through a new modification.

Computational results show promising performance on benchmark tests.

Abstract

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. It is an outer approximation algorithm and is based on solving norm-minimizing scalarizations. Unlike Pascolleti-Serafini scalarization used in the literature for similar purposes, it does not involve a direction parameter. Therefore, the algorithm is free of direction-biasedness. We also propose a modification of the algorithm by introducing a suitable compact subset of the upper image, which helps in proving for the first time the finiteness of an algorithm for convex vector optimization. The computational performance of the algorithms is illustrated using some of the benchmark test problems, which shows promising results in comparison to a similar algorithm that is based on Pascoletti-Serafini scalarization.