Optimality conditions and duality in terms of convexificators for multiobjective bilevel programming problem with equilibrium constraints

This paper is devoted to the investigation of a nonsmooth multiobjective bilevel programming problem with equilibrium constraints ((MBPP) for short) in terms of convexificators in finite-dimensional spaces. We present necessary optimality conditions for the local weak efficient solution to such problem. Under the Mangasarian-Fromovitz and generalized standard Abadie type constraint qualification in the sense of convexificators, we establish as an application the Wolfe and Mond-Weir type dual problem for the problem (MBPP). Besides, we provide strong and weak duality theorems for the original problem and its Wolfe and Mond-Weir type dual problem under suitable assumptions on the partial derivative*-convexity and the upper semi-regularity of objective and constraint functions. Illustrative examples are also proposed to demonstrate the main results of the paper.