An easy path to convex analysis and applications:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[San Rafael, Calif.]
Morgan & Claypool
2014
|
| Series: | Synthesis lectures on mathematics and statistics
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | XVI, 202 S. graph. Darst. |
| ISBN: | 9781627052375 9781627052382 |
Staff View
MARC
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Record in the Search Index
| _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 |
| author_GND | (DE-588)104316845 |
| author_facet | Morduchovič, Boris S. Nam, Nguyen Mau |
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| author_sort | Morduchovič, Boris S. |
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| 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 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027358035 |
| oclc_num | 870203236 |
| open_access_boolean | |
| owner | DE-29T DE-20 |
| owner_facet | DE-29T DE-20 |
| physical | XVI, 202 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Morgan & Claypool |
| record_format | marc |
| 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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