This book provides a unified and insightful treatment of deterministic global optimization. It introduces theoretical and algorithmic advances that address the computation and characterization of global optima, determine valid lower and upper bounds on the global minima and maxima, and enclose all solutions of nonlinear constrained systems of equations.
Among its special features, the book: * Introduces the fundamentals of deterministic global optimization; * Provides a thorough treatment of decomposition-based global optimization approaches for biconvex and bilinear problems; * Covers global optimization methods for generalized geometric programming problems * Presents in-depth global optimization algorithms for general twice continuously differentiable nonlinear problems; * Provides a detailed treatment of global optimization methods for mixed-integer nonlinear problems; * Develops global optimization approaches for the enclosure of all solutions of nonlinear constrained systems of equations; * Includes many important applications from process design, synthesis, control, and operations, phase equilibrium, design under uncertainty, parameter estimation, azeotrope prediction, structure prediction in clusters and molecules, protein folding, and peptide docking.
Audience: This book can be used as a textbook in graduate-level courses and as a desk reference for researchers in all branches of engineering and applied science, applied mathematics, industrial engineering, operations research, computer science, economics, computational chemistry and molecular biology.
Preface. 1. Introduction. 2. Basic Concepts of Global Optimization. Part I: Biconvex and Bilinear Problems. 3. The GOP Primal-Relaxed Dual Decomposition Approach: Theory. 4. The GOP Approach: Implementation and Computational Studies. 5. The GOP Approach in Bilevel Linear and Quadratic Problems. 6. The GOP Approach in Phase and Chemical Equilibrium Problems. 7. The GOP Approach: Distributed Implementation. Part II: Signomial Problems. 8. Generalized Geometric Programming: Theory. 9. Generalized Geometric Programming: Computational Studies. Part III: Towards General Twice Differentiable NLPs. 10. From Biconvex to General Twice Differentiable NLPs. 11. The alphaBB For Box Constrained Twice-Differentiable NLPs: Theory. 12. The alphaBB for Constrained Twice-Differentiable NLPs: Theory. 13. Computational Studies of the alphaBB Approach. 14. Global Optimization in Microclusters. 15. The alphaBB Approach in Molecular Structure Prediction. 16. The alphaBB Approach in Protein Folding. 17. The alphaBB Approach in Peptide Docking. 18. The alphaBB Approach in Batch Design Under Uncertainty. 19. The alphaBB Approach in Parameter Estimation. Part IV: Nonlinear and Mixed-Integer Optimization. 20. Introduction to Nonlinear and Mixed-Integer Optimization. 21. The SMIN-alphaBB Approach: Theory and Computations. 22. The GMIN-alphaBB Approach: Theory and Computations. Part V: Nonlinear Constrained Systems of Equations. 23. All Solutions of Nonlinear Constrained Systems of Equations. 24. Locating all Homogeneous Azeotropes. References. Index.