Numerical Optimization : Theoretical and Practical Aspects / by J. Frédéric Bonnans, J. Charles Gilbert, Claude Lemaréchal, Claudia A. Sagastizábal
(Universitext)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer , 2003 |
| 本文言語 | 英語 |
| 大きさ | XIII, 423 p. 7 illus : online resource |
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| 内容注記 | 1 General Introduction 2 Basic Methods 3 Line-Searches 4 Newtonian Methods 5 Conjugate Gradient 6 Special Methods 7 Some Theory of Nonsmooth Optimization 8 Some Methods in Nonsmooth Optimization 9 Bundle Methods. The Quest of Descent 10 Decomposition and Duality 11 Background 12 Local Methods for Problems with Equality Constraints 13 Local Methods for Problems with Equality and Inequality Constraints 14 Exact Penalization 15 Globalization by Line-Search 16 Quasi-Newton Versions 17 Linearly Constrained Optimization and Simplex Algorithm 18 Linear Monotone Complementarity and Associated Vector Fields 19 Predictor-Corrector Algorithms 20 Non-Feasible Algorithms 21 Self-Duality 22 One-Step Methods 23 Complexity of Linear Optimization Problems with Integer Data 24 Karmarkar’s Algorithm References |
|---|---|
| 一般注記 | Starting with illustrative real-world examples, this book exposes in a tutorial way algorithms for numerical optimization: fundamental ones (Newtonian methods, line-searches, trust-region, sequential quadratic programming, etc.), as well as more specialized and advanced ones (nonsmooth optimization, decomposition techniques, and interior-point methods). Most of these algorithms are explained in a detailed manner, allowing straightforward implementation. Theoretical aspects are addressed with care, often using minimal assumptions. The present version contains substantial changes with respect to the first edition. Part I on unconstrained optimization has been completed with a section on quadratic programming. Part II on nonsmooth optimization has been thoroughly reorganized and expanded. In addition, nontrivial application problems have been inserted, in the form of computational exercises. These should help the reader to get a better understanding of optimization methods beyond their abstract description, by addressing important features to be taken into account when passing to implementation of any numerical algorithm. This level of detail is intended to familiarize the reader with some of the crucial questions of numerical optimization: how algorithms operate, why they converge, difficulties that may be encountered and their possible remedies. |
| 著者標目 | *Bonnans, J. Frédéric author Gilbert, J. Charles author Lemaréchal, Claude author Sagastizábal, Claudia A. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algorithms LCSH:Computer science -- Mathematics 全ての件名で検索 LCSH:Numerical analysis LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Operations research LCSH:Management science FREE:Mathematics FREE:Optimization FREE:Operations Research, Management Science FREE:Calculus of Variations and Optimal Control; Optimization FREE:Numerical Analysis FREE:Algorithm Analysis and Problem Complexity FREE:Mathematics of Computing |
| 分 類 | DC23:519.6 |
| 巻冊次 | ISBN:9783662050781 
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| ISBN | 9783662050781 |
| URL | http://dx.doi.org/10.1007/978-3-662-05078-1 |
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※2021年9月12日以降