Convex optimization theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Mass.
Athena Scientific
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Titel auf dem Buchrücken: Convex optmization theory |
| Physical Description: | X, 246 S. graph. Darst. |
| ISBN: | 1886529310 9781886529311 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804174729661120512 |
|---|---|
| adam_text | Contents
9
1. Basic Concepts of Convex Analysis..............................p. 1
1.1. Convex Sets and Functions.................................p. 2
1.1.1. Convex Functions.....................................p. 5
1.1.2. Closedness and Semicontinuity........................p. 9
1.1.3. Operations with Convex Functions.....................p.ll
1.1.4. Characterizations of Differentiable Convex Functions . . p. 13
1.2. Convex and Affine Hulls...................................p. 19
1.3. Relative Interior and Closure.............................p. 23
1.3.1. Calculus of Relative Interiors and Closures..........p. 28
1.3.2. Continuity of Convex Functions.......................p. 35
1.3.3. Closures of Functions................................p. 37
1.4. Recession Cones...........................................p. 43
1.4.1. Directions of Recession of a Convex Function.........p. 50
1.4.2. Nonemptiness of Intersections of Closed Sets.........p. 57
1.4.3. Closedness Under Linear Transformations..............p. 64
1.5. Hyperplanes...............................................p. 67
1.5.1. Hyperplane Separation ...............................p. 68
1.5.2. Proper Hyperplane Separation.........................p. 73
1.5.3. Nonvertical Hyperplane Separation....................p. 80
1.6. Conjugate Functions ......................................p. 82
1.7. Summary...................................................p. 89
2. Basic Concepts of Polyhedral Convexity.........................p. 91
2.1. Extreme Points............................................p. 92
2.2. Polar Cones...............................................p. 99
2.3. Polyhedral Sets and Functions...........................p. 102
2.3.1. Polyhedral Cones and Farkas’ Lemma.................p. 102
2.3.2. Structure of Polyhedral Sets.......................p. 104
2.3.3. Polyhedral Functions...............................p. 109
2.4. Polyhedral Aspects of Optimization .....................p. Ill
3. Basic Concepts of Convex Optimization........................p. 115
3.1. Constrained Optimization................................p. 116
3.2. Existence of Optimal Solutions..........................p.118
iii
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| any_adam_object | 1 |
| author | Bertsekas, Dimitri P. 1942- |
| author_GND | (DE-588)171165519 |
| author_facet | Bertsekas, Dimitri P. 1942- |
| author_role | aut |
| author_sort | Bertsekas, Dimitri P. 1942- |
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| building | Verbundindex |
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| discipline | Mathematik |
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| id | DE-604.BV042574804 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:05:01Z |
| institution | BVB |
| isbn | 1886529310 9781886529311 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028008288 |
| oclc_num | 746128360 |
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| owner | DE-29T DE-703 DE-188 |
| owner_facet | DE-29T DE-703 DE-188 |
| physical | X, 246 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Athena Scientific |
| record_format | marc |
| spelling | Bertsekas, Dimitri P. 1942- Verfasser (DE-588)171165519 aut Convex optimization theory Dimitri P. Bertsekas Convex optmization theory Belmont, Mass. Athena Scientific 2009 X, 246 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Titel auf dem Buchrücken: Convex optmization theory Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028008288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bertsekas, Dimitri P. 1942- Convex optimization theory Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4137027-2 |
| title | Convex optimization theory |
| title_alt | Convex optmization theory |
| title_auth | Convex optimization theory |
| title_exact_search | Convex optimization theory |
| title_full | Convex optimization theory Dimitri P. Bertsekas |
| title_fullStr | Convex optimization theory Dimitri P. Bertsekas |
| title_full_unstemmed | Convex optimization theory Dimitri P. Bertsekas |
| title_short | Convex optimization theory |
| title_sort | convex optimization theory |
| topic | Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Konvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028008288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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