Numerical optimization techniques:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Springer
1985
|
| Series: | Translations series in mathematics and engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | EST: Metody rešenija ekstremal'nych zadach i ich primenenie v sistemach optimizacij <engl.>. - Aus d. Russ. übers. |
| Physical Description: | xiv, 558 Seiten Diagramme |
| ISBN: | 0387909494 0911575073 3540909494 |
Staff View
MARC
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| 240 | 1 | 0 | |a Metody rešenija ekstremal'nych zada i ich primenenie v sistemach optimizacij |
| 245 | 1 | 0 | |a Numerical optimization techniques |c Yurij G. Evtushenko |
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Record in the Search Index
| _version_ | 1804114857329426432 |
|---|---|
| adam_text | CONTENTS
Foreword xi
Preface xiii
Notation 1
Chapter 1. An Introduction to Optimization Theory 6
1. Convex Sets and Convex Functions 6
2. Differentiability of Convex Functions 16
3. Necessary and Sufficient Conditions of a Local
Extremum of Functions of Many Variables 27
4. Necessary and Sufficient Conditions for a
Minimum of Functions on Sets 34
5. Properties of Minimax Problems 40
6. Conditions for a Minimum in Nonlinear Programming
Problems Without Differentiability 60
7. Conditions for a Minimum in Nonlinear Programming
Problems With Differentiability 75
8. Necessary Conditions for a Minimum in
Optimal Control Problems 94
Chapter 2. Convergence Theorems and Their Application to the
Investigation of Numerical Methods 107
1. Stability of the First Order Approximation 107
2. The Method of Lyapunov Functions 115
3. Theorems on Convergence of Iterative
Processes 129
4. Convergence of Processes Generated by
Multivalued Mappings 145
5. Methods for Solving Systems of Nonlinear
Equations 152
6. Numerical Methods for Finding a Minimax 177
(viii) CONTENTS
Chapter 3. The Penalty Function Method 196
1. The Exterior Penalty Function Method 197
2. Estimation of Accuracy 215
3. The Cost Function Parametrization Method 234
4. The Interior Penalty Function Method 245
5. The Linearization Method 255
Chapter 4. Numerical Methods for Solving
Nonlinear Programming Problems
Using Modified Lagrangians 264
1. The Simplest Modification of the Lagrangian 265
2. Modified Lagrangians 279
3. Proof of Convergence for the Simple
Iteration Method 286
4. Solution of Convex Programming Problems 301
5. Reduction to a Maximin Problem 310
6. Reduction to a Minimax Problem 321
Chapter 5. Relaxation Methods for Solving
Nonlinear Programming Problems 330
1. Application of the Reduced Gradient Method
to Solving Problems With Equality Type
Constraints 330
2. A Generalization of the Reduced Gradient
Method 336
3. A Discrete Version of the Reduced
Gradient Method 351
4. The Conditional Gradient Method 355
5. The Gradient Projection Method 361
Chapter 6. Numerical Methods for Solving
Optimal Control Problems 364
1. Basic Computational Formulas 367
2. Necessary and Sufficient Conditions
for A Minimum 383
(ix) CONTENTS
3. Numerical Methods Based on the Reduction
to Nonlinear Programming Problems 388
4. Discrete Minimum Principles 398
5. Numerical Methods Based on Discrete
Minimum Principle 418
6. Some Generalizations 423
7. Examples of Numerical Computations 434
8. An Application to Differential Games 455
Chapter 7. Search for Global Solutions 465
1. The General Notion of Coverings 466
2. Covering a Parallelepiped 474
3. Solution of Nonlinear Programming Problems 491
4. Solution of Systems of Algebraic Equations 502
5. Solution of Minimax Problems 505
6. Solution of Multicriteria Problems 509
Appendix I. Differentiability 517
Appendix II. Some Properties of Matrices 522
Appendix III. Some Properties of Mappings 530
Notes and Comments 533
References 539
Index 554
List of Forthcoming Publications 559
Transliteration Table 561
|
| any_adam_object | 1 |
| author | Evtušenko, Jurij Gavrilovič 1938- |
| author_GND | (DE-588)1089353154 |
| author_facet | Evtušenko, Jurij Gavrilovič 1938- |
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| author_sort | Evtušenko, Jurij Gavrilovič 1938- |
| author_variant | j g e jg jge |
| building | Verbundindex |
| bvnumber | BV000395830 |
| classification_rvk | SK 870 |
| classification_tum | MAT 916f |
| ctrlnum | (OCoLC)241443985 (DE-599)BVBBV000395830 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000395830 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:13:23Z |
| institution | BVB |
| isbn | 0387909494 0911575073 3540909494 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000245831 |
| oclc_num | 241443985 |
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| physical | xiv, 558 Seiten Diagramme |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series2 | Translations series in mathematics and engineering |
| spelling | Evtušenko, Jurij Gavrilovič 1938- (DE-588)1089353154 aut Metody rešenija ekstremal'nych zada i ich primenenie v sistemach optimizacij Numerical optimization techniques Yurij G. Evtushenko New York Springer 1985 xiv, 558 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Translations series in mathematics and engineering EST: Metody rešenija ekstremal'nych zadach i ich primenenie v sistemach optimizacij <engl.>. - Aus d. Russ. übers. Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Optimierung (DE-588)4043664-0 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Nichtlineare Optimierung (DE-588)4128192-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000245831&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evtušenko, Jurij Gavrilovič 1938- Numerical optimization techniques Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4043664-0 (DE-588)4128130-5 |
| title | Numerical optimization techniques |
| title_alt | Metody rešenija ekstremal'nych zada i ich primenenie v sistemach optimizacij |
| title_auth | Numerical optimization techniques |
| title_exact_search | Numerical optimization techniques |
| title_full | Numerical optimization techniques Yurij G. Evtushenko |
| title_fullStr | Numerical optimization techniques Yurij G. Evtushenko |
| title_full_unstemmed | Numerical optimization techniques Yurij G. Evtushenko |
| title_short | Numerical optimization techniques |
| title_sort | numerical optimization techniques |
| topic | Nichtlineare Optimierung (DE-588)4128192-5 gnd Optimierung (DE-588)4043664-0 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Nichtlineare Optimierung Optimierung Numerisches Verfahren |
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