Convex analysis and nonlinear optimization: theory and examples
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2010
|
| Edition: | 2. ed. [softcover version of original hardcover edition 2006] |
| Series: | CMS books in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 310 S. 235 mm x 155 mm, 486 g |
| ISBN: | 9781441921277 1441921273 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804149247521587200 |
|---|---|
| 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
Xl
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
|
| any_adam_object | 1 |
| author | Borwein, Jonathan M. 1951-2016 Lewis, Adrian S. |
| author_GND | (DE-588)115617884 |
| author_facet | Borwein, Jonathan M. 1951-2016 Lewis, Adrian S. |
| author_role | aut aut |
| author_sort | Borwein, Jonathan M. 1951-2016 |
| author_variant | j m b jm jmb a s l as asl |
| building | Verbundindex |
| bvnumber | BV040251026 |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)802344144 (DE-599)DNB1008416657 |
| discipline | Mathematik |
| edition | 2. ed. [softcover version of original hardcover edition 2006] |
| format | Book |
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| id | DE-604.BV040251026 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:20:00Z |
| institution | BVB |
| isbn | 9781441921277 1441921273 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025106993 |
| oclc_num | 802344144 |
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| owner_facet | DE-739 |
| physical | XII, 310 S. 235 mm x 155 mm, 486 g |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | CMS books in mathematics |
| spelling | Borwein, Jonathan M. 1951-2016 Verfasser (DE-588)115617884 aut Convex analysis and nonlinear optimization theory and examples Jonathan M. Borwein ; Adrian S. Lewis 2. ed. [softcover version of original hardcover edition 2006] New York, NY Springer 2010 XII, 310 S. 235 mm x 155 mm, 486 g txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics Konvexe Analysis (DE-588)4138566-4 gnd rswk-swf Konvexe Funktion (DE-588)4139679-0 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s Konvexe Funktion (DE-588)4139679-0 s 1\p DE-604 Konvexe Analysis (DE-588)4138566-4 s 2\p DE-604 Lewis, Adrian S. Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025106993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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 Lewis, Adrian S. Convex analysis and nonlinear optimization theory and examples Konvexe Analysis (DE-588)4138566-4 gnd Konvexe Funktion (DE-588)4139679-0 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4138566-4 (DE-588)4139679-0 (DE-588)4128192-5 |
| 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 | Konvexe Analysis (DE-588)4138566-4 gnd Konvexe Funktion (DE-588)4139679-0 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Konvexe Analysis Konvexe Funktion Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025106993&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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