Deterministic Global Optimization: Theory, Methods and Applications

Pirmais vāks
Springer Science & Business Media, 2013. gada 9. marts - 742 lappuses
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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INTRODUCTION
1
THE GOP APPROACH IMPLEMENTATION AND COMPUTATIONAL STUDIES
141
THE GOP APPROACH IN BILEVEL LINEAR AND QUADRATIC PROBLEMS
173
DISTRIBUTED IMPLEMENTATION
243
Signomial Problems
257
COMPUTATIONAL STUDIES
289
FROM BICONVEX TO GENERAL TWICE DIFFERENTIABLE NLPS
309
THEORY315
315
THE ABB APPROACH IN PEPTIDE DOCKING
481
THE ABB APPROACH IN BATCH DESIGN UNDER UNCERTAINTY
507
THE aBB APPROACH IN PARAMETER ESTIMATION
543
Nonlinear and MixedInteger Optimization
571
THE SMINαBB APPROACH THEORY AND COMPUTATIONS
587
THE GMINaBB APPROACH THEORY AND COMPUTATIONS
617
Nonlinear Constrained Systems of Equations
641
LOCATING ALL HOMOGENEOUS AZEOTROPES
667

THE aBB FOR CONSTRAINED TWICE DIFFERENTIABLE NLPS THEORY
333
COMPUTATIONAL STUDIES OF THE ABB APPROACH
377
GLOBAL OPTIMIZATION IN MICROCLUSTERS
403
THE ABB APPROACH IN MOLECULAR STRUCTURE PREDICTION
435
References
699
xiii
736
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