Ebook: Deterministic Global Optimization: Theory, Methods and Applications

The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad­ vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con­ strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob­ lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.

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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.

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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.
Content:
Front Matter....Pages i-xvii
Introduction....Pages 1-32
Basic Concepts of Global Optimization....Pages 33-64
Front Matter....Pages 65-65
The GOP Primal — Relaxed Dual Decomposition Approach : Theory....Pages 67-139
The GOP Approach : Implementation and Computational Studies....Pages 141-172
The GOP Approach in Bilevel Linear and Quadratic Problems....Pages 173-191
The GOP Approach in Phase and Chemical Equilibrium Problems....Pages 193-242
The GOP Approach : Distributed Implementation....Pages 243-253
Front Matter....Pages 255-255
Generalized Geometric Programming : Theory....Pages 257-287
Generalized Geometric Programming : Computational Studies....Pages 289-306
Front Matter....Pages 307-307
From Biconvex to General Twice Differentiable NLPs....Pages 309-314
The ?BB Approach for Box Constrained Twice-Differentiable NLPs : Theory....Pages 315-331
The ?BB Approach for General Constrained Twice-Differentiable NLPs : Theory....Pages 333-375
Computational Studies of the ?BB Approach....Pages 377-402
Global Optimization in Microclusters....Pages 403-433
The ?BB Approach in Molecular Structure Prediction....Pages 435-450
The ?BB Approach in Protein Folding....Pages 451-480
The ?BB Approach in Peptide Docking....Pages 481-505
The ?BB Approach in Batch Design under Uncertainty....Pages 507-541
The ?BB Approach in Parameter Estimation....Pages 543-568
Front Matter....Pages 569-569
Introduction to Nonlinear and Mixed-Integer Optimization....Pages 571-585
Front Matter....Pages 569-569
The SMIN-?BB Approach : Theory and Computations....Pages 587-615
The GMIN-?BB Approach : Theory and Computations....Pages 617-638
Front Matter....Pages 639-639
All Solutions of Nonlinear Constrained Systems of Equations....Pages 641-666
Locating All Homogeneous Azeotropes....Pages 667-698
Back Matter....Pages 699-742

---

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.
Content:
Front Matter....Pages i-xvii
Introduction....Pages 1-32
Basic Concepts of Global Optimization....Pages 33-64
Front Matter....Pages 65-65
The GOP Primal — Relaxed Dual Decomposition Approach : Theory....Pages 67-139
The GOP Approach : Implementation and Computational Studies....Pages 141-172
The GOP Approach in Bilevel Linear and Quadratic Problems....Pages 173-191
The GOP Approach in Phase and Chemical Equilibrium Problems....Pages 193-242
The GOP Approach : Distributed Implementation....Pages 243-253
Front Matter....Pages 255-255
Generalized Geometric Programming : Theory....Pages 257-287
Generalized Geometric Programming : Computational Studies....Pages 289-306
Front Matter....Pages 307-307
From Biconvex to General Twice Differentiable NLPs....Pages 309-314
The ?BB Approach for Box Constrained Twice-Differentiable NLPs : Theory....Pages 315-331
The ?BB Approach for General Constrained Twice-Differentiable NLPs : Theory....Pages 333-375
Computational Studies of the ?BB Approach....Pages 377-402
Global Optimization in Microclusters....Pages 403-433
The ?BB Approach in Molecular Structure Prediction....Pages 435-450
The ?BB Approach in Protein Folding....Pages 451-480
The ?BB Approach in Peptide Docking....Pages 481-505
The ?BB Approach in Batch Design under Uncertainty....Pages 507-541
The ?BB Approach in Parameter Estimation....Pages 543-568
Front Matter....Pages 569-569
Introduction to Nonlinear and Mixed-Integer Optimization....Pages 571-585
Front Matter....Pages 569-569
The SMIN-?BB Approach : Theory and Computations....Pages 587-615
The GMIN-?BB Approach : Theory and Computations....Pages 617-638
Front Matter....Pages 639-639
All Solutions of Nonlinear Constrained Systems of Equations....Pages 641-666
Locating All Homogeneous Azeotropes....Pages 667-698
Back Matter....Pages 699-742
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