Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators

In this paper, we consider optimization problems with equilibrium constraints. We study the Wolfe‐type dual problem for the optimization problems with equilibrium constraints under the convexity assumptions using convexificators. A Mond–Weir‐type dual problem is also formulated and studied for the optimization problems with equilibrium constraints under convexity and generalized convexity assumptions using convexificators. Weak duality theorems are established to relate the optimization problems with equilibrium constraints and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification.