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Volume 6, Issue 6, 1 December 2022, Pages 605-618
Abstract. In many real world problems, the simultaneous minimization of many certain goals is needed. Such problems lead to vector optimization problems with variable domination structure, where the domination structure is given by a set-valued map. In this framework, one of the most important solution concepts is the concept of nondominated points. In this paper, we propose a steepest descent-like method for computing nondominated solutions of smooth unconstrained vector optimization problems with variable domination structure. We obtain that every accumulation point of the generated sequence satisfies a first order necessary condition. We discuss the consequence of this fact in the convex case.
How to Cite this Article:
Gemayqzel Bouza, Christiane Tammer, A steepest descent-like method for vector optimization problems with variable domination structure, J. Nonlinear Var. Anal. 6 (2022), 605-618.