Convex functions: constructions, characterizations and counterexamples
Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programm...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2010
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 109 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (x, 521 pages) |
| ISBN: | 9781139087322 |
| DOI: | 10.1017/CBO9781139087322 |
Internformat
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| 505 | 8 | |a Why convex? -- Convex functions on Euclidean spaces -- Finer structure of Euclidean spaces -- Convex functions on Banach spaces -- Duality between smoothness and strict convexity -- Further analytic topics -- Barriers and Legendre functions -- Convex functions and classifications of Banach spaces -- Monotone operators and the Fitzpatrick function -- Further remarks and notes | |
| 520 | |a Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level | ||
| 650 | 4 | |a Convex functions | |
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Datensatz im Suchindex
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| author | Borwein, Jonathan M. 1951-2016 |
| author_GND | (DE-588)115617884 (DE-588)140343938 |
| author_facet | Borwein, Jonathan M. 1951-2016 |
| author_role | aut |
| author_sort | Borwein, Jonathan M. 1951-2016 |
| author_variant | j m b jm jmb |
| building | Verbundindex |
| bvnumber | BV043942012 |
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| contents | Why convex? -- Convex functions on Euclidean spaces -- Finer structure of Euclidean spaces -- Convex functions on Banach spaces -- Duality between smoothness and strict convexity -- Further analytic topics -- Barriers and Legendre functions -- Convex functions and classifications of Banach spaces -- Monotone operators and the Fitzpatrick function -- Further remarks and notes |
| ctrlnum | (ZDB-20-CBO)CR9781139087322 (OCoLC)851064582 (DE-599)BVBBV043942012 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139087322 |
| format | Electronic eBook |
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| spelling | Borwein, Jonathan M. 1951-2016 Verfasser (DE-588)115617884 aut Convex functions constructions, characterizations and counterexamples Jonathan M. Borwein, Jon D. Vanderwerff Cambridge Cambridge University Press 2010 1 online resource (x, 521 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 109 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Why convex? -- Convex functions on Euclidean spaces -- Finer structure of Euclidean spaces -- Convex functions on Banach spaces -- Duality between smoothness and strict convexity -- Further analytic topics -- Barriers and Legendre functions -- Convex functions and classifications of Banach spaces -- Monotone operators and the Fitzpatrick function -- Further remarks and notes Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level Convex functions Banach spaces Geometry, Non-Euclidean Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Konvexe Funktion (DE-588)4139679-0 s 2\p DE-604 Vanderwerff, Jon D. Sonstige (DE-588)140343938 oth Erscheint auch als Druck-Ausgabe 978-0-521-85005-6 https://doi.org/10.1017/CBO9781139087322 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Borwein, Jonathan M. 1951-2016 Convex functions constructions, characterizations and counterexamples Why convex? -- Convex functions on Euclidean spaces -- Finer structure of Euclidean spaces -- Convex functions on Banach spaces -- Duality between smoothness and strict convexity -- Further analytic topics -- Barriers and Legendre functions -- Convex functions and classifications of Banach spaces -- Monotone operators and the Fitzpatrick function -- Further remarks and notes Convex functions Banach spaces Geometry, Non-Euclidean Konvexe Funktion (DE-588)4139679-0 gnd |
| subject_GND | (DE-588)4139679-0 (DE-588)4123623-3 |
| title | Convex functions constructions, characterizations and counterexamples |
| title_auth | Convex functions constructions, characterizations and counterexamples |
| title_exact_search | Convex functions constructions, characterizations and counterexamples |
| title_full | Convex functions constructions, characterizations and counterexamples Jonathan M. Borwein, Jon D. Vanderwerff |
| title_fullStr | Convex functions constructions, characterizations and counterexamples Jonathan M. Borwein, Jon D. Vanderwerff |
| title_full_unstemmed | Convex functions constructions, characterizations and counterexamples Jonathan M. Borwein, Jon D. Vanderwerff |
| title_short | Convex functions |
| title_sort | convex functions constructions characterizations and counterexamples |
| title_sub | constructions, characterizations and counterexamples |
| topic | Convex functions Banach spaces Geometry, Non-Euclidean Konvexe Funktion (DE-588)4139679-0 gnd |
| topic_facet | Convex functions Banach spaces Geometry, Non-Euclidean Konvexe Funktion Lehrbuch |
| url | https://doi.org/10.1017/CBO9781139087322 |
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