Disjunctive Programming

The subject of this book is Disjunctive Programming, a technique and a discipline initiated by the author in the early 1970's, which has become the main tool for solving nonconvex optimization problems, like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution of the state of the art of Integer Programming that took place between 1990-2005. In the last 45 years hundreds of articles have appeared on disjunctive programming, but there is no book yet describing the discipline; so the present volume will fill a glaring gap. Mixed integer optimization problems are solved through a combination of implicit enumeration (branch and bound) and convexification (cutting plane) techniques. The convexification procedures are based on the use of disjunctions, possibly combined with modularization. Disjunctive Programming is optimization under disjunctive constraints, like either/or and related logical conditions applied to inequalities. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capacity and improved solution methods for integer and combinatorial optimization problems.