From Biconvex to General Twice Differentiable NLPs

Abstract

In this chapter we present an important theoretical development (Liu and Floudas, 1993) that allows us to extend the GOP global optimization approach from biconvex and bilinear problems into general constrained twice-differentiable nonlinear optimization problems. This theoretical development provides the link between the GOP algorithm and the αBB global optimization approach, which is our focus on Part III of this book. Section 10.1 presents the theoretical developments that lead from the GOP to the αBB global optimization approach. Section 10.2 presents a brief introduction to the calculation of the a parameters and one alternative for obtaining rigorous bounds on the a parameters for general constrained twice differentiable nonlinear optimization problems. The material presented in this chapter is based on the work of Liu and Floudas (1993) and Maranas and Floudas (1994b).