Convex analysis and nonlinear optimization: theory and examples
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
2006
|
| Edition: | second edition |
| Series: | Canadian Mathematical Society: CMS books in mathematics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 310 Seiten |
| ISBN: | 0387295704 9780387295701 9781441921277 |
Staff View
MARC
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| 245 | 1 | 0 | |a Convex analysis and nonlinear optimization |b theory and examples |c Jonathan M. Borwein ; Adrian S. Lewis |
| 250 | |a second edition | ||
| 264 | 1 | |a New York |b Springer |c 2006 | |
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| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Background 1
1.1 Euclidean Spaces 1
1.2 Symmetric Matrices 9
2 Inequality Constraints 15
2.1 Optimality Conditions 15
2.2 Theorems of the Alternative 23
2.3 Max functions 28
3 Fenchel Duality 33
3.1 Subgradients and Convex Functions 33
3.2 The Value Function 43
3.3 The Fenchel Conjugate 49
4 Convex Analysis 65
4.1 Continuity of Convex Functions 65
4.2 Fenchel Biconjugation 76
4.3 Lagrangian Duality 88
5 Special Cases 97
5.1 Polyhedral Convex Sets and Functions 97
5.2 Functions of Eigenvalues 104
5.3 Duality for Linear and Semidefinite Programming 109
5.4 Convex Process Duality 114
6 Nonsmooth Optimization 123
6.1 Generalized Derivatives 123
6.2 Regularity and Strict Differentiability 130
6.3 Tangent Cones 137
6.4 The Limiting Subdifferential 145
xi
xii Contents
7 Karush Kuhn Tucker Theory 153
7.1 An Introduction to Metric Regularity 153
7.2 The Karush Kuhn Tucker Theorem 160
7.3 Metric Regularity and the Limiting Subdifferential 166
7.4 Second Order Conditions 172
8 Fixed Points 179
8.1 The Brouwer Fixed Point Theorem 179
8.2 Selection and the Kakutani Fan Fixed Point Theorem . . . 190
8.3 Variational Inequalities 200
9 More Nonsmooth Structure 213
9.1 Rademacher s Theorem 213
9.2 Proximal Normals and Chebyshev Sets 218
9.3 Amenable Sets and Prox Regularity 228
9.4 Partly Smooth Sets 233
10 Postscript: Infinite Versus Finite Dimensions 239
10.1 Introduction 239
10.2 Finite Dimensionality 241
10.3 Counterexamples and Exercises 244
10.4 Notes on Previous Chapters 248
11 List of Results and Notation 253
11.1 Named Results 253
11.2 Notation 267
Bibliography 275
Index 289
|
| adam_txt |
Contents
Preface vii
1 Background 1
1.1 Euclidean Spaces 1
1.2 Symmetric Matrices 9
2 Inequality Constraints 15
2.1 Optimality Conditions 15
2.2 Theorems of the Alternative 23
2.3 Max functions 28
3 Fenchel Duality 33
3.1 Subgradients and Convex Functions 33
3.2 The Value Function 43
3.3 The Fenchel Conjugate 49
4 Convex Analysis 65
4.1 Continuity of Convex Functions 65
4.2 Fenchel Biconjugation 76
4.3 Lagrangian Duality 88
5 Special Cases 97
5.1 Polyhedral Convex Sets and Functions 97
5.2 Functions of Eigenvalues 104
5.3 Duality for Linear and Semidefinite Programming 109
5.4 Convex Process Duality 114
6 Nonsmooth Optimization 123
6.1 Generalized Derivatives 123
6.2 Regularity and Strict Differentiability 130
6.3 Tangent Cones 137
6.4 The Limiting Subdifferential 145
xi
xii Contents
7 Karush Kuhn Tucker Theory 153
7.1 An Introduction to Metric Regularity 153
7.2 The Karush Kuhn Tucker Theorem 160
7.3 Metric Regularity and the Limiting Subdifferential 166
7.4 Second Order Conditions 172
8 Fixed Points 179
8.1 The Brouwer Fixed Point Theorem 179
8.2 Selection and the Kakutani Fan Fixed Point Theorem . . . 190
8.3 Variational Inequalities 200
9 More Nonsmooth Structure 213
9.1 Rademacher's Theorem 213
9.2 Proximal Normals and Chebyshev Sets 218
9.3 Amenable Sets and Prox Regularity 228
9.4 Partly Smooth Sets 233
10 Postscript: Infinite Versus Finite Dimensions 239
10.1 Introduction 239
10.2 Finite Dimensionality 241
10.3 Counterexamples and Exercises 244
10.4 Notes on Previous Chapters 248
11 List of Results and Notation 253
11.1 Named Results 253
11.2 Notation 267
Bibliography 275
Index 289 |
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| any_adam_object_boolean | 1 |
| author | Borwein, Jonathan M. 1951-2016 Lewis, Adrian S. 1962- |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)63166869 (DE-599)BVBBV021786518 |
| dewey-full | 515/.8 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | second edition |
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| index_date | 2024-07-02T15:43:05Z |
| indexdate | 2024-07-09T20:44:04Z |
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| isbn | 0387295704 9780387295701 9781441921277 |
| language | English |
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| physical | xii, 310 Seiten |
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| spelling | Borwein, Jonathan M. 1951-2016 (DE-588)115617884 aut Convex analysis and nonlinear optimization theory and examples Jonathan M. Borwein ; Adrian S. Lewis second edition New York Springer 2006 xii, 310 Seiten txt rdacontent n rdamedia nc rdacarrier Canadian Mathematical Society: CMS books in mathematics 3 Analyse (wiskunde) gtt Convexe functies gtt Niet-lineaire vergelijkingen gtt Optimaliseren gtt Programação convexa larpcal Programação matemática larpcal Convex functions Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s Konvexe Funktion (DE-588)4139679-0 s DE-604 Konvexe Analysis (DE-588)4138566-4 s Lewis, Adrian S. 1962- (DE-588)107040408X aut Erscheint auch als Online-Ausgabe 978-0-387-31256-9 Canadian Mathematical Society: CMS books in mathematics 3 (DE-604)BV013248581 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014999232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borwein, Jonathan M. 1951-2016 Lewis, Adrian S. 1962- Convex analysis and nonlinear optimization theory and examples Canadian Mathematical Society: CMS books in mathematics Analyse (wiskunde) gtt Convexe functies gtt Niet-lineaire vergelijkingen gtt Optimaliseren gtt Programação convexa larpcal Programação matemática larpcal Convex functions Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Konvexe Analysis (DE-588)4138566-4 gnd Konvexe Funktion (DE-588)4139679-0 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4138566-4 (DE-588)4139679-0 |
| title | Convex analysis and nonlinear optimization theory and examples |
| title_auth | Convex analysis and nonlinear optimization theory and examples |
| title_exact_search | Convex analysis and nonlinear optimization theory and examples |
| title_exact_search_txtP | Convex analysis and nonlinear optimization theory and examples |
| title_full | Convex analysis and nonlinear optimization theory and examples Jonathan M. Borwein ; Adrian S. Lewis |
| title_fullStr | Convex analysis and nonlinear optimization theory and examples Jonathan M. Borwein ; Adrian S. Lewis |
| title_full_unstemmed | Convex analysis and nonlinear optimization theory and examples Jonathan M. Borwein ; Adrian S. Lewis |
| title_short | Convex analysis and nonlinear optimization |
| title_sort | convex analysis and nonlinear optimization theory and examples |
| title_sub | theory and examples |
| topic | Analyse (wiskunde) gtt Convexe functies gtt Niet-lineaire vergelijkingen gtt Optimaliseren gtt Programação convexa larpcal Programação matemática larpcal Convex functions Mathematical optimization Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Konvexe Analysis (DE-588)4138566-4 gnd Konvexe Funktion (DE-588)4139679-0 gnd |
| topic_facet | Analyse (wiskunde) Convexe functies Niet-lineaire vergelijkingen Optimaliseren Programação convexa Programação matemática Convex functions Mathematical optimization Nonlinear theories Nichtlineare Optimierung Konvexe Analysis Konvexe Funktion |
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