Numerical optimization theoretical and practical aspects J. Frédéric Bonnans.... Universitext.

• Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Berlin, Springer
• ISBN-13: 9783540001911
• ISBN-10: 3540001913
• Artikelnr.: 11415318

Autorenporträt

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 Research Institute for Applied Mathematics and Computer Science, 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 production, fluid dynamics, wave propagation, optimal control, energy management, etc.

Inhaltsangabe

Preliminaries
1 General Introduction
1. 1 Generalities on Optimization
1. 2 Motivation and Examples
1. 3 General Principles of Resolution
1. 4 General Convergence Theorem: Zangwill
1. 5 Generalities on Convergence
1. 6 Computing the Gradient

Part I - Unconstrained Problems
2 Basic Methods
2. 1 Existence Questions
2. 2 Optimality Conditions
2. 3 First-Order Methods
2. 4 Link with the General Descent Scheme
2. 5 Steepest-Descent Method
2. 6 Implementation
3 Line-Searches
3. 1 General Scheme
3. 2 Computing the New t
3. 3 Optimal Stepsize (for the record only)
3. 4 Modern Line-Search: Wolfe's Rule
3. 5 Other Line-Searches: Goldstein and Price, Armijo
3. 6 Implementation Considerations
4 Newtonian Methods
4. 1 Preliminaries
4. 2 Forcing Global Convergence
4. 3 Alleviating the Method
4. 4 Quasi-Newton Methods
4. 5 Global Convergence
4. 6 Local Convergence: Generalities
4. 7 Local Convergence: BFGS
5 Conjugate Gradient
5. 1 Outline of Conjugate Gradient
5. 2 Developing the Method
5. 3 Computing the Direction
5. 4 The Algorithm Seen as an Orthogonalization Process
5. 5 Application to Non-Quadratic Functions
5. 6 Relation with Quasi-Newton
6 Special Methods
6. 1 Trust-Regions
6. 2 Least-Squares Problems: Gauss-Newton
6. 3 Large-Scale Problems: Limited-Memory Quasi-Newton
6. 4 Truncated Newton

Part II - Nonsmooth Optimization
7 Some Theory of Nonsmooth Optimization
7. 1 First Elements of Convex Analysis
7. 2 Lagrangian Relaxation and Duality
7. 3 Two Convex Nondifferentiable Functions
8 Some Methods in Nonsmooth Optimization
8. 1 Why Special Methods?
8. 2 Descent Methods
8. 3 Two Black-Box Methods
9 Bundle Methods. The Quest of Descent
9. 1 Stabilization. A Primal Approach
9. 2 Some Examples of Stabilized Problems
9. 3 Penalized Bundle Methods
10 Decomposition and Duality
10. 1 Primal-Dual.