Numerical Optimization: Theoretical and Practical Aspects

Copertina anteriore
Springer Science & Business Media, 6 ott 2006 - 494 pagine

Just as in its 1st edition, this book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. Most of the algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects of the approaches chosen are also addressed with care, often using minimal assumptions.

This new edition contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical, description, when coming to actual implementation. Besides, the nonsmooth optimization part has been substantially reorganized and expanded.

 

Sommario

General Introduction
3
22
23
Basic Methods 25
24
3
37
Newtonian Methods
51
Conjugate Gradient
67
Special Methods
77
Seismic Reflection Tomography
97
Notes
250
Exact Penalization
271
Globalization by LineSearch
289
QuasiNewton Versions
323
InteriorPoint Algorithms for Linear and Quadratic
346
Linearly Constrained Optimization and Simplex
353
5 Comments
393
PredictorCorrector Algorithms 21 1 Overview
395

Introduction to Nonsmooth Optimization
109
Some Methods in Nonsmooth Optimization
119
Bundle Methods The Quest for Descent
137
Applications of Nonsmooth Optimization 161
160
Newtons Methods in Constrained Optimization
189
Local Methods for Problems with Equality Constraints
215
425
427
Complexity of Linear Optimization Problems with
451
Karmarkars Algorithm
457
References
465
Index
485
Copyright

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Informazioni sull'autore (2006)

The four authors are leading international specialists in various branches of nonlinear optimization (one of them received the Dantzig Prize). They are working - or have worked - at INRIA, the French National Institute for Research in Computer Science and Control, and they also teach in various universities and "Grandes Écoles". All of them continually collaborate with industry on problems dealing with optimization, in fields such as energy management, geoscience, life sciences, etc.

Informazioni bibliografiche