C. M. Shetty

A finitely convergent procedure for facial disjunctive programs

Abstract This paper addresses an important class of disjunctive programs called facial disjunctive programs, examples of which include the zero-one linear integer programming problem and the linear complementarity problem. Balas has characterized some fundamental properties of such problems, one of which has been used by Jeroslow to obtain a finitely convergent procedure. This paper exploits another basic property of facial disjunctive programs in order to develop an alternative finitely convergent algorithm.

Generation of Deep Cuts Using the Fundamental Disjunctive Inequality

Recall from Chapter I that our motivation in using disjunctive programming methods is to aid us in solving nonconvex problems of the type

Basic Concepts and Principles

\begin{gathered} DP: minimize (fx) \hfill \\ subject to x\varepsilon X \hfill \\ \end{gathered}

Some Specific Applications of Disjunctive Programming Problems

\begin{gathered} x \varepsilon U S_h \hfill \\ h\varepsilon H \hfill \\ \end{gathered}

The bilinear programming problem

where f: Rn → R is lower semicontinuous, X is a closed subset of the nonnegative orthant of Rn and each Sh, h e H is given by Equation (1.1).