Robust optimality conditions for multiobjective programming problems under data uncertainty and its applications - Nguyen, Thuy Thi Thu; Su, Tran Van; Linh, Dang Hong (Optimization, 2024)
In this article, we employ advanced techniques of convex analysis and $ \mathcal {C} $ C -differentiation to examine KKT-type robust necessary and sufficient optimality conditions and robust duality for an uncertain multiobjective programming problem under uncertainty sets, where $ \mathcal {C} $ C denotes the set of all $ \mathcal {G} $ G -derivatives which are positively homogeneous and convex with respect to the second argument. We first provide the robust constraint qualification of the (RCQ) type via the $ \mathcal {C} $ C -derivatives of uncertain constraint functions. We second establish KKT-type robust necessary conditions for robust (weakly) efficient solutions via the subdifferentials of $ \mathcal {C} $ C -derivatives to such problems. We third propose two new kinds of generalized $ \mathcal {C} $ C -convex functions via the subdifferentials of $ \mathcal {C} $ C -derivatives involving max-functions. Under suitable assumptions on the generalized $ \mathcal {C} $ C -convexity, KKT-type robust necessary optimality conditions become robust sufficient optimality conditions. Furthermore, we formulate as some applications a dual multiobjective programming problem to the underlying programming and examine weak, strong, and converse duality theorems for the same. Some illustrative examples are also provided for our findings.