Finitely Convergent Algorithms for Facial Disjunctive Programs with Applications to the Linear Complementarity Problem

Abstract

In our discussion of Chapter V, we had introduced a special class of disjunctive programs called facial disjunctive programs, examples of which included the zero-one linear integer programming problem and the linear complementarity problem. We had seen that for this special class of problems, it was relatively easy to generate the convex hull of feasible points. In this chapter, we will discuss two finitely convergent schemes which solve facial disjunctive programs by generating facets of the convex hull of feasible points as and when needed, until such time as either a suitable termination criterion is met or the problem is solved through the generation of the entire convex hull.