Methods of descent for nondifferentiable optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1985
|
| Schriftenreihe: | Lecture notes in mathematics
1133 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 362 S. |
| ISBN: | 3540156429 0387156429 |
Internformat
MARC
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| 100 | 1 | |a Kiwiel, Krzysztof C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Methods of descent for nondifferentiable optimization |c Krzysztof C. Kiwiel |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1985 | |
| 300 | |a VI, 362 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1133 | |
| 650 | 4 | |a Fonctions non différentiables | |
| 650 | 7 | |a Mathematische programmering |2 gtt | |
| 650 | 4 | |a Maximums et minimums | |
| 650 | 4 | |a Optimisation mathématique | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Maxima and minima | |
| 650 | 4 | |a Nondifferentiable functions | |
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| 830 | 0 | |a Lecture notes in mathematics |v 1133 |w (DE-604)BV000676446 |9 1133 | |
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Datensatz im Suchindex
| _version_ | 1805071476788822016 |
|---|---|
| adam_text |
TABLE OF CONTENTS
Page
Chapter 1. Fundamentals
1.1. Introduction 1
1.2. Basic Results of Nondifferentiable Optimization
Theory 2
1.3. A Review of Existing Algorithms and Original
Contributions of This Work 22
Chapter 2. Aggregate Subgradient Methods for Unconstrained
Convex Minimization
2.1. Introduction 44
2.2. Derivation of the Algorithm Class 44
2.3. The Basic Algorithm 57
2.4. Convergence of the Basic Algorithm 59
2.5. The Method with Subgradient Selection 71
2.6. Finite Convergence for Piecewise Linear Functions 76
2.7. Line Search Modifications 84
Chapter 3. Methods with Subgradient Locality Measures for Minimi¬
zing Nonconvex Functions
3.1. Introduction 87
3.2. Derivation of the Methods 88
3.3. The Algorithm with Subgradient Aggregation 99
3.4. Convergence 106
3.5. The Algorithm with Subgradient Selection 123
3.6. Modifications of the Methods 131
Chapter 4. Methods with Subgradient Deletion Rules for Uncon¬
strained Honconvex Minimization
4.1. Introduction 139
4.2. Derivation of the Methods 141
4.3. The Algorithm with Subgradient Aggregation . 150
4.4. Convergence 156
4.5. The Algorithm with Subgradient Selection 168
4.6. Modified Resetting Strategies 171
4.7. Simplified Versions That Neglect Linearization
Errors 185
Chapter 5. Feasible Point Methods for Convex Constrained Minimi¬
zation Problems
VI I
5.1. Introduction 190
5.2. Derivation of the Algorithm Class 191
5.3. The Algorithm with Subgradient Aggregation 205
5.4. Convergence 207
5.5. The Method with Subgradient Selection 215
5.6. Line Search Modifications 217
5.7. Phase I Phase II Methods 219
Chapter 6. Methods of Feasible Directions for Honconvex
Constrained Problems
6.1. Introduction 229
6.2. Derivation of the Methods 230
6.3. The Algorithm with Subgradient Aggregation 245
6.4. Convergence 252
6.5. The Algorithm with Subgradient Selection 264
6.6. Modifications of the Methods 269
6.7. Methods with Subgradient Deletion Rules 275
6.8. Methods That Neglect Linearization Errors 293
6.9. Phase I Phase II Methods 294
Chapter 7. Bundle Methods
7.1. Introduction 299
7.2. Derivation of the Methods 300
7.3. The Algorithm with Subgradient Aggregation 307
7.4. Convergence 3X2
7.5. The Algorithm with Subgradient Selection 318
7.6. Modified Line Search Rules and Approximation Tole¬
rance Updating Strategies 320
7.7. Extension to Nonconvex Unconstrained Problems . 335
7.8. Bundle Methods for Convex Constrained Problems . 330
7.9. Extensions to Nonconvex Constrained Problems 339
Chapter 8. Numerical Examples
8.1. Introduction 345
8.2. Numerical Results 345
References 354
Index , 361 |
| any_adam_object | 1 |
| author | Kiwiel, Krzysztof C. |
| author_facet | Kiwiel, Krzysztof C. |
| author_role | aut |
| author_sort | Kiwiel, Krzysztof C. |
| author_variant | k c k kc kck |
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| bvnumber | BV000380498 |
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| callnumber-raw | QA3 |
| callnumber-search | QA3 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| classification_tum | MAT 919f |
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| dewey-full | 511/.6 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics 510 - Mathematics |
| dewey-raw | 511/.6 510 |
| dewey-search | 511/.6 510 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000380498 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:38:26Z |
| institution | BVB |
| isbn | 3540156429 0387156429 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000235831 |
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| physical | VI, 362 S. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Kiwiel, Krzysztof C. Verfasser aut Methods of descent for nondifferentiable optimization Krzysztof C. Kiwiel Berlin [u.a.] Springer 1985 VI, 362 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1133 Fonctions non différentiables Mathematische programmering gtt Maximums et minimums Optimisation mathématique Mathematical optimization Maxima and minima Nondifferentiable functions Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Verallgemeinerte Gradientenmethode (DE-588)4187510-2 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Nichtdifferenzierbare Funktion (DE-588)4326748-8 s Optimierung (DE-588)4043664-0 s Verallgemeinerte Gradientenmethode (DE-588)4187510-2 s Lecture notes in mathematics 1133 (DE-604)BV000676446 1133 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000235831&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kiwiel, Krzysztof C. Methods of descent for nondifferentiable optimization Lecture notes in mathematics Fonctions non différentiables Mathematische programmering gtt Maximums et minimums Optimisation mathématique Mathematical optimization Maxima and minima Nondifferentiable functions Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Verallgemeinerte Gradientenmethode (DE-588)4187510-2 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4326748-8 (DE-588)4128192-5 (DE-588)4187510-2 (DE-588)4043664-0 |
| title | Methods of descent for nondifferentiable optimization |
| title_auth | Methods of descent for nondifferentiable optimization |
| title_exact_search | Methods of descent for nondifferentiable optimization |
| title_full | Methods of descent for nondifferentiable optimization Krzysztof C. Kiwiel |
| title_fullStr | Methods of descent for nondifferentiable optimization Krzysztof C. Kiwiel |
| title_full_unstemmed | Methods of descent for nondifferentiable optimization Krzysztof C. Kiwiel |
| title_short | Methods of descent for nondifferentiable optimization |
| title_sort | methods of descent for nondifferentiable optimization |
| topic | Fonctions non différentiables Mathematische programmering gtt Maximums et minimums Optimisation mathématique Mathematical optimization Maxima and minima Nondifferentiable functions Nichtdifferenzierbare Funktion (DE-588)4326748-8 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Verallgemeinerte Gradientenmethode (DE-588)4187510-2 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Fonctions non différentiables Mathematische programmering Maximums et minimums Optimisation mathématique Mathematical optimization Maxima and minima Nondifferentiable functions Nichtdifferenzierbare Funktion Nichtlineare Optimierung Verallgemeinerte Gradientenmethode Optimierung |
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| volume_link | (DE-604)BV000676446 |
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