The αBB Approach for Box Constrained Twice-Differentiable NLPs : Theory
In this chapter, we discuss the theory of the αBB for box constrained twice-differentiable nonlinear optimization problems. Section 11.1 presents the formulation of the box constrained nonlinear problems, and the transformation into a D.C. problem of special structure that leads into the Conditions (A) required by the GOP. Section 11.2 presents the important derivation of a convex lower bounding function, L, based on duality theory, and discusses all the theoretical properties that L satisfies. Section 11.3 introduces the αBB global optimization approach for box constrained twice-differentiable NLPs and presents its convergence proof. Section 11.4 presents the complexity analysis of the αBB approach. The material presented in this chapter is based on the work of Maranas and Floudas (1994a), (1994b).
KeywordsGlobal Minimum Nonlinear Optimization Problem Global Optimization Algorithm Partition Element Maximum Separation Distance
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