Verfügbarkeit: Convex analysis and nonlinear optimization

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Bibliographische Detailangaben
Titel:	Convex analysis and nonlinear optimization theory and examples
Von:	Jonathan M. Borwein ; Adrian S. Lewis
Person:	Borwein, Jonathan M. 1951-2016 aut Lewis, Adrian S. 1962-
Hauptverfassende:	Borwein, Jonathan M. 1951-2016 (VerfasserIn), Lewis, Adrian S. 1962- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York Springer 2006
Ausgabe:	second edition
Schriftenreihe:	Canadian Mathematical Society: CMS books in mathematics 3
Notation:	SK 870
Schlagwörter:	Analyse (wiskunde) Convexe functies Niet-lineaire vergelijkingen Optimaliseren Programação convexa Programação matemática Convex functions Mathematical optimization Nonlinear theories Nichtlineare Optimierung Konvexe Analysis Konvexe Funktion
Medienzugang:	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
Umfang:	xii, 310 Seiten
ISBN:	0387295704 9780387295701 9781441921277

Internformat

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Datensatz im Suchindex

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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
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author	Borwein, Jonathan M. 1951-2016 Lewis, Adrian S. 1962-
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id	DE-604.BV021786518
illustrated	Not Illustrated
indexdate	2024-12-20T12:41:45Z
institution	BVB
isbn	0387295704 9780387295701 9781441921277
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-014999232
oclc_num	63166869
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owner	DE-19 DE-BY-UBM DE-634 DE-91G DE-BY-TUM DE-29T DE-11 DE-355 DE-BY-UBR DE-20 DE-188 DE-83 DE-706
owner_facet	DE-19 DE-BY-UBM DE-634 DE-91G DE-BY-TUM DE-29T DE-11 DE-355 DE-BY-UBR DE-20 DE-188 DE-83 DE-706
physical	xii, 310 Seiten
publishDate	2006
publishDateSearch	2006
publishDateSort	2006
publisher	Springer
record_format	marc
series	Canadian Mathematical Society: CMS books in mathematics
series2	Canadian Mathematical Society: CMS books in mathematics
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_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
url	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
volume_link	(DE-604)BV013248581
work_keys_str_mv	AT borweinjonathanm convexanalysisandnonlinearoptimizationtheoryandexamples AT lewisadrians convexanalysisandnonlinearoptimizationtheoryandexamples

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