Inner approximation method for a reverse convex programming problem

In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the compleme nt of the interior of a compact convex set X. We propose an inner approxima tion method to solve the problem in the case where X is not necessarily a p olytope. The algorithm utilizes an inner approximation of X by a sequence o f polytopes to generate relaxed problems. It is shown that every accumulati on point of the sequence of optimal solutions of the relaxed problems is an optimal solution of the original problem.