Convex Analysis and Minimization Algorithms I : Fundamentals / by Jean-Baptiste Hiriart-Urruty, Claude Lemarechal
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 1993. |
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
| 出版年 | 1993 |
書誌詳細を非表示
| 書誌ID | OB01019089 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Table of Contents Part I -- I. Convex Functions of One Real Variable -- II. Introduction to Optimization Algorithms -- III. Convex Sets -- IV. Convex Functions of Several Variables -- V. Sublinearity and Support Functions -- VI. Subdifferentials of Finite Convex Functions -- VII. Constrained Convex Minimization Problems: Minimality Conditions, Elements of Duality Theory -- VIII. Descent Theory for Convex Minimization: The Case of Complete Information -- Appendix: Notations -- 1 Some Facts About Optimization -- 2 The Set of Extended Real Numbers -- 3 Linear and Bilinear Algebra -- 4 Differentiation in a Euclidean Space -- 5 Set-Valued Analysis -- 6 A Bird's Eye View of Measure Theory and Integration -- Bibliographical Comments -- References. License restrictions may limit access Summary: Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books |
| 著者標目 | *Hiriart-Urruty, Jean-Baptiste Lemarechal, Claude SpringerLink (Online service) |
| 統一書名標目 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, |
| 件 名 | LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Mathematics LCSH:Operations research LCSH:Management science LCSH:System theory LCSH:Control theory FREE:Calculus of Variations and Optimization FREE:Applications of Mathematics FREE:Operations Research, Management Science FREE:Systems Theory, Control |
| 分 類 | LCC:QA402.5-402.6 LCC:QA315-316 DC23:519.6 DC23:515.64 |
| 巻冊次 | ISBN:9783662027967 RefWorks出力（各巻） print ; ISBN:9783642081613 RefWorks出力（各巻） print ; ISBN:9783540568506 RefWorks出力（各巻） print ; ISBN:9783662027974 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
| 所蔵情報へのリンク | Convex analysis and minimization algorithms / Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal ; 1 : gw - 2 : us |
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