Sequential Convexification in Reverse Convex and Disjunctive Programming.
Management science research rept.,
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Pagination or Media Count:
This paper is about a property of certain combinatorial structures, called sequential convexifiability, shown by Balas 1974, 1979 to hold for facial disjunctive programs. Sequential convexifiability means that the convex hull of a nonconvex set defined by a collection of constraints can be generated by imposing the constraints one by one, sequentially, and generating each time the convex hull of the resulting set. This document extends the class of problems considered to disjunctive programs with infinitely many terms, also known as reverse convex programs, and give necessary and sufficient conditions for the solution sets of such problems to be sequentially convexifiable. The authors point out important classes of problems in addition to facial disjunctive programs for instance, reverse convex programs with equations only for which the conditions are always satisfied. Finally, given, are examples of disjunctive programs for which the conditions are violated, and so the procedure breaks down.
- Operations Research