Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

Logic-based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems Sangbum Lee and Ignacio E. Grossmann Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA15213 November 28, 2003 (submitted to Annals of Operations Research) Abstract This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic -based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixedinteger programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.