Date of Original Version
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.compchemeng.2009.10.016
Abstract or Description
This paper is concerned with global optimization of Bilinear and Concave Generalized Disjunctive Programs. A major objective is to propose a procedure to find relaxations that yield strong lower bounds. We first present a general framework for obtaining a hierarchy of linear relaxations for nonconvex Generalized Disjunctive Programs (GDP). This framework combines linear relaxation strategies proposed in the literature for nonconvex MINLPs with the results of the work by Sawaya and Grossmann (2009) for Linear GDPs. We further exploit the theory behind Disjunctive Programming by proposing several rules to guide more efficiently the generation of relaxations by considering the particular structure of the problems. Finally, we show through a set of numerical examples that these new relaxations can substantially strengthen the lower bounds for the global optimum, often leading to a significant reduction of the number of nodes when used within a spatial branch and bound framework.
Computers and Chemical Engineering, 34, 6, 914-930.