Optimality Conditions in Uncertain Multi-Objective Optimization Problems with a Variable Domination Structure

Abstract

In this paper, we first establish some new properties of a kind of nonlinear scalarization function. Second, based on set approaches, we introduce a class of new definitions of robustness for an uncertain multi-objective optimization problem with a variable domination structure. Finally, by applying the scalarization method, we obtain the necessary and sufficient optimality conditions of the robustness for the uncertain multi-objective optimization problem with a variable domination structure in a more general setting. Some of the obtained results extend and imply the corresponding ones in recent literature.