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Newton-Type Methods for Optimization and Variational Problems / by Alexey F. Izmailov, Mikhail V. Solodov
(Springer Series in Operations Research and Financial Engineering. ISSN:21971773)
版 | 1st ed. 2014. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2014 |
本文言語 | 英語 |
大きさ | XIX, 573 p. 30 illus., 1 illus. in color : online resource |
著者標目 | *Izmailov, Alexey F author Solodov, Mikhail V author SpringerLink (Online service) |
件 名 | LCSH:Operations research LCSH:Management science LCSH:Mathematical optimization FREE:Operations Research, Management Science FREE:Continuous Optimization FREE:Optimization |
一般注記 | 1. Elements of optimization theory and variational analysis -- 2. Equations and unconstrained optimization -- 3. Variational problems: local methods -- 4. Constrained optimization: local methods -- 5. Variational problems: globalization of convergence -- 6. Constrained optimization: globalization of convergence -- 7. Degenerate problems with non-isolated solutions -- A. Miscellaneous material This book presents comprehensive state-of-the-art theoretical analysis of the fundamental Newtonian and Newtonian-related approaches to solving optimization and variational problems. A central focus is the relationship between the basic Newton scheme for a given problem and algorithms that also enjoy fast local convergence. The authors develop general perturbed Newtonian frameworks that preserve fast convergence and consider specific algorithms as particular cases within those frameworks, i.e., as perturbations of the associated basic Newton iterations. This approach yields a set of tools for the unified treatment of various algorithms, including some not of the Newton type per se. Among the new subjects addressed is the class of degenerate problems. In particular, the phenomenon of attraction of Newton iterates to critical Lagrange multipliers and its consequences as well as stabilized Newton methods for variational problems and stabilized sequential quadratic programming for optimization. This volume will be useful to researchers and graduate students in the fields of optimization and variational analysis HTTP:URL=https://doi.org/10.1007/978-3-319-04247-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319042473 |
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電子リソース |
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EB00237153 |
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データ種別 | 電子ブック |
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分 類 | LCC:T57.6-57.97 LCC:T55.4-60.8 DC23:3 |
書誌ID | 4000115016 |
ISBN | 9783319042473 |
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※2017年9月4日以降