On Robust Nonsmooth Semi-Infinite Multiobjective Optimization Problems Involving Intersection of Closed Sets

This paper investigates robust optimality and mixed-type duality for robust semi-infinite multiobjective optimization problems involving the intersection of closed sets within the robust optimization framework (UP), using limiting subdifferentials, where uncertainties are incorporated into both the objective and inequality constraint functions. Using the concepts of advanced variational analysis techniques, we first derive the robust Karush-Kuhn-Tucker (KKT) necessary optimality conditions for its robust counterpart (RP) under the assumption of robust limiting constraint qualification (RLCQ). We further establish robust sufficient optimality conditions using the notions of generalized convexity and generalized pseudoquasiconvexity. Additionally, we formulate a mixed-type robust dual model corresponding to the primal problem and analyze robust weak and strong duality. To validate our theoretical findings, we present numerical examples that demonstrate the applicability and effectiveness of the proposed approach.