A finite cutting plane method for solving linear programs with an additional reverse convex constraint

The paper deals with linear programs with an additional reverse convex constraint. If the feasible region of this problem is nonempty and the objective function to be minimized is bounded below on it, then the problem has a finite minimum obtained on an at most one-dimensional face of the polyhedron as well. This paper presents a finite cutting plane method using convexity and disjunctive cuts for solving the considered problem. The metod is based upon a procedure which, for a given nonnegative integer q, either finds such an at most q-dimensional face of the original polyhedron which has a point feasible to the cuts generated previously or proves that there exists no such a face. Computational experience is also provided.