Deterministic Global Optimization: Theory, Methods and Applications

B́a trước
Springer Science & Business Media, 9 thg 3, 2013 - 742 trang
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
BASIC CONCEPTS OF GLOBAL OPTIMIZATION
33
THEORY
67
IMPLEMENTATION AND COMPUTATIONAL STUDIES
141
THE GOP APPROACH IN BILEVEL LINEAR AND QUADRATIC PROBLEMS
173
THE GOP APPROACH IN PHASE AND CHEMICAL EQUILIBRIUM PROBLEMS
193
DISTRIBUTED IMPLEMENTATION
243
THEORY
257
THE CYBB APPROACH IN MOLECULAR STRUCTURE PREDICTION
435
THE CyBB APPROACH IN PROTEIN FOLDING
451
THE QBB APPROACH IN PEPTIDE DOCKING
481
THE CYBB APPROACH IN BATCH DESIGN UNDER UNCERTAINTY
507
THE CYBB APPROACH IN PARAMETER ESTIMATION
543
Nonlinear and MixedInteger Optimization
571
THEORY AND COMPUTATIONS
587
THEORY AND COMPUTATIONS
617

COMPUTATIONAL STUDIES
289
FROM BICONVEX TO GENERAL TWICE DIFFERENTIABLE NLPS
309
THEORY315
315
THEORY
333
COMPUTATIONAL STUDIES OF THE OBB APPROACH
377
GLOBAL OPTIMIZATION IN MICROCLUSTERS
403
Nonlinear Constrained Systems of Equations
641
LOCATING ALL HOMOGENEOUS AZEOTROPES
667
References
699
xiii
736
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