2022/07/07 by Andrea Wagner, Wagner, Andrea, Fırdevs Ulus +7 · 1 citation
Computer Science · Engineering · Mathematics · #90B50 #90C25 #90C29 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2207.03200
openalex publication_date 2022/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [Ararat et al. 2022, Doerfler et al. 2021, Loehne et al. 2014]. They provide a polyhedral inner and outer approximation of the upper image that have a Hausdorff distance of at most ε. However, it is well known (see [Ulus, 2018]), that for some unbounded problems such polyhedral approximations do not exist. In this paper, we will propose a generalized solution concept, called an (ε,δ)--solution, that allows also to consider unbounded CVOPs. It is based on additionally bounding the recession cones of the inner and outer polyhedral approximations of the upper image in a meaningful way. An algorithm is proposed that computes such δ--outer and δ--inner approximations of the recession cone of the upper image. In combination with the results of [Loehne et al. 2014] this provides a primal and a dual algorithm that allow to compute (ε,δ)--solutions of (potentially unbounded) CVOPs. Numerical examples are provided.