A mathematical view of interior point methods in convex optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM ; MPS
2001
|
| Series: | MPS SIAM series on optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vii, 117 Seiten |
| ISBN: | 0898715024 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV014054326 | ||
| 003 | DE-604 | ||
| 005 | 20200316 | ||
| 007 | t | ||
| 008 | 011211s2001 |||| 00||| eng d | ||
| 020 | |a 0898715024 |9 0-89871-502-4 | ||
| 035 | |a (OCoLC)248043360 | ||
| 035 | |a (DE-599)BVBBV014054326 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91 |a DE-91G |a DE-703 |a DE-634 |a DE-83 |a DE-384 | ||
| 050 | 0 | |a QA402.5 | |
| 082 | 0 | |a 519.3 | |
| 084 | |a SK 870 |0 (DE-625)143265: |2 rvk | ||
| 084 | |a 90C25 |2 msc | ||
| 084 | |a MAT 915f |2 stub | ||
| 084 | |a 90C51 |2 msc | ||
| 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 | |
| 650 | 4 | |a Konvexe Optimierung - Innere-Punkte-Methode | |
| 650 | 0 | 7 | |a Innere-Punkte-Methode |0 (DE-588)4352322-5 |2 gnd |9 rswk-swf |
| 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 | 1 | |a Innere-Punkte-Methode |0 (DE-588)4352322-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009624139 | ||
Record in the Search Index
| _version_ | 1804128914514116608 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Renegar, James 1955- |
| author_GND | (DE-588)1146016166 |
| author_facet | Renegar, James 1955- |
| author_role | aut |
| author_sort | Renegar, James 1955- |
| author_variant | j r jr |
| building | Verbundindex |
| bvnumber | BV014054326 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.5 |
| callnumber-search | QA402.5 |
| callnumber-sort | QA 3402.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 |
| classification_tum | MAT 915f |
| ctrlnum | (OCoLC)248043360 (DE-599)BVBBV014054326 |
| dewey-full | 519.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 |
| dewey-search | 519.3 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01684nam a2200433 c 4500</leader><controlfield tag="001">BV014054326</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200316 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">011211s2001 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0898715024</subfield><subfield code="9">0-89871-502-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)248043360</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014054326</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA402.5</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.3</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 870</subfield><subfield code="0">(DE-625)143265:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">90C25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 915f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">90C51</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Renegar, James</subfield><subfield code="d">1955-</subfield><subfield code="0">(DE-588)1146016166</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A mathematical view of interior point methods in convex optimization</subfield><subfield code="c">James Renegar</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">A mathematical view of interior-point methods in convex optimization</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Philadelphia</subfield><subfield code="b">SIAM ; MPS</subfield><subfield code="c">2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">vii, 117 Seiten</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">MPS SIAM series on optimization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Konvexe Optimierung - Innere-Punkte-Methode</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Innere-Punkte-Methode</subfield><subfield code="0">(DE-588)4352322-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konvexe Optimierung</subfield><subfield code="0">(DE-588)4137027-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Konvexe Optimierung</subfield><subfield code="0">(DE-588)4137027-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Innere-Punkte-Methode</subfield><subfield code="0">(DE-588)4352322-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009624139</subfield></datafield></record></collection> |
| id | DE-604.BV014054326 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:49Z |
| institution | BVB |
| isbn | 0898715024 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009624139 |
| oclc_num | 248043360 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-384 |
| owner_facet | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-703 DE-634 DE-83 DE-384 |
| physical | vii, 117 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | SIAM ; MPS |
| record_format | marc |
| 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 |
| work_keys_str_mv | AT renegarjames amathematicalviewofinteriorpointmethodsinconvexoptimization |