A Norm Minimization-Based Convex Vector Optimization Algorithm

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 Pascoletti-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.

Automated summary

We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. The algorithm is free of direction-biasedness as it does not involve a direction parameter. We also prove for the first time the finiteness of an algorithm for convex vector optimization by introducing a suitable compact subset of the upper image. The computational performance of the algorithm shows promising results compared to a similar algorithm based on Pascoletti-Serafini scalarization.