RLT-Based Global Optimization Algorithms for Nonconvex Polynomial Programming Problems

Abstract

Thus far, we have considered the generation of tight relaxations leading to the convex hull representation for linear and nonlinear (polynomial) discrete mixed-integer programming problems using the Reformulation-Linearization Technique (RLT). It turns out that because of its natural facility to enforce relationships between different polynomial terms, RLT can be gainfully employed to obtain global optimal solutions for continuous, nonconvex, polynomial programming problems as well. In this context, although a hierarchy of nested, tighter relaxations can be generated, except in special cases, convex hull representations are not necessarily produced at any particular level, or even in the limit as the number of applications tends to infinity. (See Chapter 8 for a discussion on a special case of bilinear programming problems for which RLT does produce convex hull or convex envelope representations.)