Optimal value function in semi-infinite programming (Q1093526)

We provide a systematic approach to the main topics in linear semi- infinite programming by means of a new methodology based on the many properties of the subdifferential mapping and the closure of a given convex function. In particular, we deal with the duality gap problem and its relation with the discrete approximation of the semi-infinite program. Moreover, we have precised the conditions that allow us to eliminate the duality gap by introducing a perturbation in the primal objective function. As a byproduct, we supply different extensions of well-known results concerning the subdifferential mapping.