A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality

Abstract In this paper, we study a first-order solution method for particular class of set optimization problems where the concept is given by approach. We consider case in which set-valued objective mapping identified finite number continuously differentiable selections. The corresponding problem then equivalent to find optimistic solutions vector under uncertainty with set. develop optimality conditions these types and introduce two concepts critical points. Furthermore, propose descent provide convergence result points satisfying previously derived. Some numerical examples illustrating performance are also discussed. This paper modified polished version Chapter 5 dissertation Quintana (On relations: scalarization approach algorithms, Martin-Luther-Universität Halle-Wittenberg, 2020).