A mathematical view of interior point methods in convex optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
SIAM ; MPS
2001
|
| Schriftenreihe: | MPS SIAM series on optimization
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 117 Seiten |
| ISBN: | 0898715024 |
Internformat
MARC
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| 100 | 1 | |a Renegar, James |d 1955- |0 (DE-588)1146016166 |4 aut | |
| 245 | 1 | 0 | |a A mathematical view of interior point methods in convex optimization |c James Renegar |
| 246 | 1 | 3 | |a A mathematical view of interior-point methods in convex optimization |
| 264 | 1 | |a Philadelphia |b SIAM ; MPS |c 2001 | |
| 300 | |a vii, 117 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a MPS SIAM series on optimization | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: A mathematical view of interior point methods in convex optimization
Autor: Renegar, James
Jahr: 2001
Contents
Preface vii
1 Preliminaries 1
1.1 Linear Algebra.............................. 2
1.2 Gradients................................. 5
1.3 Hessians................................. 9
1.4 Convexity................................ 11
1.5 Fundamental Theorems of Calculus................... 14
1.6 Newton s Method............................ 18
2 Basic Interior-Point Method Theory 21
2.1 Intrinsic Inner Products......................... 21
2.2 Self-Concordant Functional ...................... 23
2.2.1 Introduction........................ 23
2.2.2 Self-Concordancy and Newton s Method......... 27
2.2.3 Other Properties...................... 31
2.3 Barrier Functional ........................... 35
2.3.1 Introduction........................ 35
2.3.2 Analytic Centers...................... 38
2.3.3 Optimal Barrier Functionals................ 39
2.3.4 Other Properties...................... 40
2.3.5 Logarithmic Homogeneity................. 41
2.4 Primal Algorithms............................ 43
2.4.1 Introduction........................ 43
2.4.2 The Barrier Method.................... 45
2.4.3 The Long-Step Barrier Method.............. 49
2.4.4 A Predictor-Corrector Method............... 52
2.5 Matters of Definition........................... 54
3 Conic Programming and Duality 65
3.1 Conic Programming........................... 65
3.2 Classical Duality Theory ........................ 68
3.3 The Conjugate Functional........................ 75
3.4 Duality of the Central Paths....................... 81
vi_________________________________________________________Contents
3.5 Self-Scaled (or Symmetrie) Cones ................... 83
3.5.1 Introduction........................ 83
3.5.2 An Important Remark on Notation ............ 85
3.5.3 Scaling Points....................... 86
3.5.4 Gradients and Norms ................... 90
3.5.5 A Useful Theorem..................... 95
3.6 The Nesterov-Todd Directions..................... 97
3.7 Primal-Dual Path-Following Methods.................. 102
3.7.1 Measures of Proximity................... 102
3.7.2 An Algorithm ....................... 104
3.7.3 Another Algorithm..................... 106
3.8 A Primal-Dual Potential-Reduction Method .............. 108
3.8.1 The Potential Function...................108
3.8.2 TheAlgorithm.......................110
3.8.3 The Analysis........................Ill
Bibliography 115
Index 117
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik |
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| id | DE-604.BV014054326 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:49Z |
| institution | BVB |
| isbn | 0898715024 |
| language | English |
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| physical | vii, 117 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | SIAM ; MPS |
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| series2 | MPS SIAM series on optimization |
| spelling | Renegar, James 1955- (DE-588)1146016166 aut A mathematical view of interior point methods in convex optimization James Renegar A mathematical view of interior-point methods in convex optimization Philadelphia SIAM ; MPS 2001 vii, 117 Seiten txt rdacontent n rdamedia nc rdacarrier MPS SIAM series on optimization Konvexe Optimierung - Innere-Punkte-Methode Innere-Punkte-Methode (DE-588)4352322-5 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 s Innere-Punkte-Methode (DE-588)4352322-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009624139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Renegar, James 1955- A mathematical view of interior point methods in convex optimization Konvexe Optimierung - Innere-Punkte-Methode Innere-Punkte-Methode (DE-588)4352322-5 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4352322-5 (DE-588)4137027-2 |
| title | A mathematical view of interior point methods in convex optimization |
| title_alt | A mathematical view of interior-point methods in convex optimization |
| title_auth | A mathematical view of interior point methods in convex optimization |
| title_exact_search | A mathematical view of interior point methods in convex optimization |
| title_full | A mathematical view of interior point methods in convex optimization James Renegar |
| title_fullStr | A mathematical view of interior point methods in convex optimization James Renegar |
| title_full_unstemmed | A mathematical view of interior point methods in convex optimization James Renegar |
| title_short | A mathematical view of interior point methods in convex optimization |
| title_sort | a mathematical view of interior point methods in convex optimization |
| topic | Konvexe Optimierung - Innere-Punkte-Methode Innere-Punkte-Methode (DE-588)4352322-5 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Konvexe Optimierung - Innere-Punkte-Methode Innere-Punkte-Methode Konvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009624139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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