An easy path to convex analysis and applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[San Rafael, Calif.]
Morgan & Claypool
2014
|
| Schriftenreihe: | Synthesis lectures on mathematics and statistics
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XVI, 202 S. graph. Darst. |
| ISBN: | 9781627052375 9781627052382 |
Internformat
MARC
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| 020 | |a 9781627052382 |9 978-1-62705-238-2 | ||
| 035 | |a (OCoLC)870203236 | ||
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| 245 | 1 | 0 | |a An easy path to convex analysis and applications |c Boris S. Mordukhovich ; Nguyen Mau Nam |
| 264 | 1 | |a [San Rafael, Calif.] |b Morgan & Claypool |c 2014 | |
| 300 | |a XVI, 202 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Synthesis lectures on mathematics and statistics |v 14 | |
| 650 | 0 | 7 | |a Konvexe Optimierung |0 (DE-588)4137027-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konvexe Optimierung |0 (DE-588)4137027-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Nam, Nguyen Mau |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027358035 | ||
Datensatz im Suchindex
| _version_ | 1804152279391010816 |
|---|---|
| adam_text | An Easy Path to
Convex Analysis and Applications
Boris S Mordukhovich
Wayne State University
Nguyen Mau Nam
Portland State University
SYNTHESIS LECTURES ON MATHEMATICS AND STATISTICS #14
Contents
Preface xi
Acknowledgments xiii
List of Symbols xv
1 Convex Sets and Functions 1
1 1 Preliminaries 1
1 2 Convex Sets 5
1 3 Convex Functions 10
1 4 Relative Interiors of Convex Sets 21
1 5 The Distance Function 28
1 6 Exercises for Chapter 1 32
2 Subdifferential Calculus 37
2 1 Convex Separation 37
2 2 Normals to Convex Sets 42
2 3 Lipschitz Continuity of Convex Functions 49
2 4 Subgradients of Convex Functions 53
2 5 Basic Calculus Rules 61
2 6 Subgradients of Optimal Value Functions 70
2 7 Subgradients of Support Functions 75
2 8 Fenchel Conjugates 77
2 9 Directional Derivatives 82
2 10 Subgradients of Supremum Functions 86
2 11 Exercises for Chapter 2 90
3 Remarkable Consequences of Convexity 95
3 1 Characterizations of Differentiability 95
3 2 Caratheodory Theorem and Farkas Lemma 97
3 3 Radon Theorem and Helly Theorem 102
3 4 Tangents to Convex Sets 103
3 5 Mean Value Theorems 106
3 6 Horizon Cones 108
3 7 Minimal Time Functions and Minkowski Gauge Ill
3 8 Subgradients of Minimal Time Functions 117
3 9 Nash Equilibrium 120
3 10 Exercises for Chapter 3 124
4 Applications to Optimization and Location Problems 129
4 1 Lower Semicontinuity and Existence of Minimizers 129
4 2 Optimality Conditions 135
4 3 Subgradient Methods in Convex Optimization 140
4 4 The Fermat-Torricelli Problem 146
45A Generalized Fermat-Torricelli Problem 154
46A Generalized Sylvester Problem 168
4 7 Exercises for Chapter 4 178
Solutions and Hints for Exercises 183
Bibliography 195
Authors’Biographies 199
Index
|
| any_adam_object | 1 |
| author | Morduchovič, Boris S. Nam, Nguyen Mau |
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| author_facet | Morduchovič, Boris S. Nam, Nguyen Mau |
| author_role | aut aut |
| author_sort | Morduchovič, Boris S. |
| author_variant | b s m bs bsm n m n nm nmn |
| building | Verbundindex |
| bvnumber | BV041914386 |
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| callnumber-sort | QA 3639.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)870203236 (DE-599)GBV777074338 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041914386 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:08:11Z |
| institution | BVB |
| isbn | 9781627052375 9781627052382 |
| language | English |
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| owner_facet | DE-29T DE-20 |
| physical | XVI, 202 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Morgan & Claypool |
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| series2 | Synthesis lectures on mathematics and statistics |
| spelling | Morduchovič, Boris S. Verfasser (DE-588)104316845 aut An easy path to convex analysis and applications Boris S. Mordukhovich ; Nguyen Mau Nam [San Rafael, Calif.] Morgan & Claypool 2014 XVI, 202 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Synthesis lectures on mathematics and statistics 14 Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 s DE-604 Nam, Nguyen Mau Verfasser aut DE-601 pdf/application http://www.gbv.de/dms/ilmenau/toc/777074338.PDF Inhaltsverzeichnis HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027358035&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Morduchovič, Boris S. Nam, Nguyen Mau An easy path to convex analysis and applications Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4137027-2 |
| title | An easy path to convex analysis and applications |
| title_auth | An easy path to convex analysis and applications |
| title_exact_search | An easy path to convex analysis and applications |
| title_full | An easy path to convex analysis and applications Boris S. Mordukhovich ; Nguyen Mau Nam |
| title_fullStr | An easy path to convex analysis and applications Boris S. Mordukhovich ; Nguyen Mau Nam |
| title_full_unstemmed | An easy path to convex analysis and applications Boris S. Mordukhovich ; Nguyen Mau Nam |
| title_short | An easy path to convex analysis and applications |
| title_sort | an easy path to convex analysis and applications |
| topic | Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Konvexe Optimierung |
| url | http://www.gbv.de/dms/ilmenau/toc/777074338.PDF http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027358035&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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