Year: 2023
Type: article
Abstract: . 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 [Ç. Ararat, F. Ulus, and M. Umer, J. Optim. Theory Appl., 194 (2022), pp. 681–712], [D. Dörfler, A. Löhne, C. Schneider, and B. Weißing, Optim. Methods Softw., 37 (2022), pp. 1006–1026], [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713–736]. They provide a polyhedral inner and outer approximation of the upper image that have a Hausdorff distance of at most [Formula: see text]. However, it is well known (see [F. Ulus, J. Global Optim., 72 (2018), pp. 731–742]), that for some unbounded problems such polyhedral approximations do not exist. In this paper, we will propose a generalized solution concept, called an [Formula: see text]–solution, that allows one to also 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 [Formula: see text]–outer and [Formula: see text]–inner approximations of the recession cone of the upper image. In combination with the results of [A. Löhne, B. Rudloff, and F. Ulus, J. Global Optim., 60 (2014), pp. 713–736] this provides a primal and a dual algorithm that allow one to compute [Formula: see text]–solutions of (potentially unbounded) CVOPs. Numerical examples are provided.
Source: SIAM Journal on Optimization
DOI: 10.1137/22m1507693
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387580397