On some nonsmooth equilibrium constrained minimization models using epiderivative

In this article, we explore duality problems of Wolfe and Mond-Weir type, tailored for mathematical programming problems that encompass non-smooth functions and equilibrium constraints, denoted by the abbreviation NSMPEC. This investigation is grounded in the realm of real Banach spaces. We will begin by presenting, conditions that serve as a sufficient basis for achieving optimality within the (NSMPEC) framework. Specifically, these conditions require the objective and constraint functions to exhibit higher-order strong invexity at the specific point under consideration. We also extend our research to formulate and prove the weak and strong duality theorems in the sense of the original problem and its dual. However, the assumptions required for this theorem assume some conditions on the higher-order strong invexity of the objective and constraint functions. To demonstrate the practical importance of the established results, we present a number of practical examples.