A conceptual method for solving generalized semi-infinite programming problems via global optimization by exact discontinuous penalization

We consider a generalized semi-infinite programming problem (GSIP) with one semi-infinite constraint where the index set depends on the variable to be minimized. Keeping in mind the integral global optimization method of Zheng and Chew and its modifications we would like to outline theoretical considerations for determining coarse approximations of a solution of (GSIP) via global optimization of an exact discontinuous penalty approach. We consider an auxiliary parametric semi-infinite programming problem and the behavior of its marginal functional. In so doing we extend the theory of robust analysis to study robustness of marginal functions and robustness of set valued mappings with given structures.