Deterministic Global Optimization

Theory, Methods and Applications

By: Christodoulos A. Floudas

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Hardcover | 31 December 1999

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764 Pages

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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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Preface
Introduction	p. 1
Basic Concepts of Global Optimization	p. 33
Biconvex and Bilinear Problems
The GOP Primal - Relaxed Dual Decomposition Approach: Theory	p. 67
The GOP Approach: Implementation and Computational Studies	p. 141
The GOP Approach in Bilevel Linear and Quadratic Problems	p. 173
The GOP Approach in Phase and Chemical Equilibrium Problems	p. 193
The GOP Approach : Distributed Implementation	p. 243
Signomial Problems
Generalized Geometric Programming: Theory	p. 257
Generalized Geometric Programming: Computational Studies	p. 289
Towards General Twice Differentiable NLPs
From Biconvex to General Twice Differentiable NLPs	p. 309
The [alpha]BB for Box Constrained Twice-Differentiable NLPs: Theory	p. 315
The [alpha]BB for Constrained Twice-Differentiable NLPs: Theory	p. 333
Computational Studies of the [alpha]BB Approach	p. 377
Global Optimization in Microclusters	p. 403
The [alpha]BB Approach in Molecular Structure Prediction	p. 435
The [alpha]BB Approach in Protein Folding	p. 451
The [alpha]BB Approach in Peptide Docking	p. 481
The [alpha]BB Approach in Batch Design Under Uncertainty	p. 507
The [alpha]BB Approach in Parameter Estimation	p. 543
Nonlinear and Mixed-Integer Optimization
Introduction to Nonlinear and Mixed-Integer Optimization	p. 571
The SMIN-[alpha]BB Approach: Theory and Computations	p. 587
The GMIN-[alpha]BB Approach: Theory and Computations	p. 617
Nonlinear Constrained Systems of Equations
All Solutions of Nonlinear Constrained Systems of Equations	p. 641
Locating all Homogeneous Azeotropes	p. 667
References	p. 699
Table of Contents provided by Blackwell. All Rights Reserved.

Deterministic Global Optimization

Theory, Methods and Applications

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Hardcover

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