Optimality and Duality for Robust Nonsmooth Semidefinite Multiobjective Programming Problems Using Convexificators

This article investigates robust optimality and duality for a class of nonsmooth semidefinite multiobjective programming problems with uncertain data (in short, UNSMP) via convexificators. Using the properties of convexificators, we deduce Fritz John (in short, FJ)-type and Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions for UNSMP. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNSMP. Furthermore, we present the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNSMP. Several illustrative non-trivial examples are furnished to demonstrate the significance of the established results.