Disjunctive Programming: Properties of the Convex Hull of Feasible Points

In this paper we characterize the convex hull of feasible points for a disjunctive program, a class of problems which subsumes pure and mixed integer programs and many other nonconvex programming problems. Two representations are given for the convex hull of feasible points. each of which provides linear programming equivalents of the disjunctive program. The first one involves a number of new variables proportional to the number of terms in the disjunctive normal form of the logical constraints; the second one involves only the original variables and the facets of the convex hull. Among other results, we give necessary and sufficient conditions for an inequality to define a facet of the convex hull of feasible points. For the class of disjunctive programs that we call facial, we establish a property which makes it possible to obtain the convex hull of points satisfying n disjunctions, in a sequence of it steps, where each step generates the convex hull of points satisfying one disjunction only. 1998 Published by Elsevier Science B.V. All rights reserved. Kqwords: Lift-and-project; Sequential convexification; Facial disjunctive programs; Reverse polars