A method for characterizing the solution set of nonconvex optimization problems via their dual problems

In this paper, we present a method for charaterizing the solution set of nonconvex optimization problems via their dual problems. In fact, the constrainted optimization problem which is considerd has pseudoconvex and locally Lipschitz functions, which are not necessarily convex and smooth, and include a wide class of non-convex non-smooth functions. In the proposed method, a dual problem is formulated to characterizations of the solution set of the primal problem in a mixed type of Wolfe type and Mond-Weir type. First, we introduce some of the properties of the Lagrangian functions associated to these problems and then we explain the proof of the characterization of their solution sets.