Numerical Optimization

Theoretical and Practical Aspects
2. Auflage 2006
ISBN: 978-3-540-35445-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 494 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1570 g

Reihe: Universitext

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Bonnans, Joseph-Frédéric

Sagastizábal, Claudia A.

Gilbert, Jean Charles

Lemarechal, Claude

Fachgebiete

• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Programmierung: Methoden und Allgemeines
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Unconstrained Problems.- General Introduction.- Basic Methods.- Line-Searches.- Newtonian Methods.- Conjugate Gradient.- Special Methods.- A Case Study: Seismic Reection Tomography.- Nonsmooth Optimization.- to Nonsmooth Optimization.- Some Methods in Nonsmooth Optimization.- Bundle Methods. The Quest for Descent.- Applications of Nonsmooth Optimization.- Computational Exercises.- Newton's Methods in Constrained Optimization.- Background.- Local Methods for Problems with Equality Constraints.- Local Methods for Problems with Equality and InequalityConstraints.- Exact Penalization.- Globalization by Line-Search.- Quasi-Newton Versions.- Interior-Point Algorithms for Linear and QuadraticOptimization.- Linearly Constrained Optimization and SimplexAlgorithm.- Linear Monotone Complementarity and Associated Vector Fields.- Predictor-Corrector Algorithms.- Non-Feasible Algorithms.- Self-Duality.- One-Step Methods.- Complexity of Linear Optimization Problems with Integer Data.- Karmarkar's Algorithm.

Über Autor(innen)

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.