Wagner, A.Ulus, FirdevsRudloff, B.Kováčová, G.Hey, N.2024-03-082024-03-082023-10-121052-6234https://hdl.handle.net/11693/114435This 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 [\c C. 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 ε. 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 (ε,δ)-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 δ-outer and δ-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 (ε,δ)-solutions of (potentially unbounded) CVOPs. Numerical examples are provided.enCC BY 4.0 DEED (Attribution 4.0 International)Convex vector optimizationUnbounded problemsApproximation algorithmApproximation of conesArticle10.1137/22M15076931095-7189