The linearization method for constrained optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Springer series in computational mathematics
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | VIII, 147 S. |
| ISBN: | 3540570373 0387570373 |
Staff View
MARC
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| 100 | 1 | |a Pšeničnyj, Boris N. |d 1937-2000 |e Verfasser |0 (DE-588)126888256 |4 aut | |
| 240 | 1 | 0 | |a Metod linearizacii |
| 245 | 1 | 0 | |a The linearization method for constrained optimization |c B. N. Pshenichnyj |
| 246 | 1 | 3 | |a The linearization method for constraint optimization |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a VIII, 147 S. | ||
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Record in the Search Index
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| adam_text | Contents
1. Convex and Quadratic Programming 1
1.1 Introduction 1
1.1.1 The Linearization Algorithm 1
1.1.2 Convergence of the Algorithm 3
1.1.3 General Remarks 4
1.1.4 Notation 5
1.2 Necessary Conditions for a Minimum and Duality 6
1.2.1 Convex Sets 7
1.2.2 Convex Functions 7
1.2.3 Foundations of Convex Programming 10
1.2.4 Duality in Convex Programming 15
1.2.5 Necessary Conditions for Extrema. General Problem 16
1.2.6 Necessary Conditions for Extrema: Second Order Conditions .. 18
1.2.7 Minimax Problems 18
1.2.8 Penalty Functions 19
1.3 Quadratic Programming Problems 22
1.3.1 Conjugate Gradient Method 23
1.3.2 Conjugate Gradient Algorithm 25
1.3.3 Existence of a Solution 25
1.3.4 Necessary Conditions for an Extremum and the Dual
Problem 28
1.3.5 Application, Projection onto a Subspace 30
1.3.6 Algorithm for the Quadratic Programming Problem 31
1.3.7 Computational Aspects 37
1.3.8 Algorithms for Simple Constraints. Generalization 41
2. The Linearization Method 43
2.1 The General Algorithm 43
2.1.1 Main Assumptions 44
2.1.2 Formulation of the Algorithm 44
2.1.3 Convergence of the Algorithm 45
2.1.4 Computational Aspects 49
2.1.5 Generalizations 51
2.1.6 The Linear Programming Problem 53
2.1.7 The Linearization Method with Equality Type Constraints 57
viii Contents
2.1.8 Simple Constraints 58
2.1.9 Choice of Parameters in the Linearization Method.
Modified Algorithm 60
2.2 Resolution of Systems of Equations and Inequalities 65
2.2.1 The Auxiliary Problem 66
2.2.2 The Algorithm 66
2.2.3 Convergence of the Algorithm 67
2.3 Acceleration of the Convergence of the Linearization Method 75
2.3.1 Main Assumptions 75
2.3.2 Local Analysis of the Auxiliary Problem 76
2.3.3 Preliminary Lemmas 81
2.3.4 The Linearization Algorithm and Acceleration of
Convergence 84
2.3.5 Linear Transformations of the Problem 87
2.3.6 Modifications of the Linearization Method 90
3. The Discrete Minimax Problem and Algorithms 99
3.1 The Discrete Minimax Problem 99
3.1.1 The Auxiliary Problem 100
3.1.2 Some Bounds 102
3.1.3 Algorithms 104
3.1.4 Algorithm for Ak = In 106
3.1.5 Acceleration of Convergence in the Convex Case 111
3.2 The Dual Algorithm for Convex Programming Problems 114
3.2.1 The Dual Algorithm 115
3.2.2 Bounds on the Rate of Convergence 118
3.2.3 An Algorithm for Convex Programming Problems 123
3.3 Algorithms and Examples 129
3.3.1 The Linearization Method 129
3.3.2 The Accelerated Linearization Method 132
3.3.3 Examples of Calculations 134
Appendix: Comments on the Literature 143
References 145
|
| any_adam_object | 1 |
| author | Pšeničnyj, Boris N. 1937-2000 |
| author_GND | (DE-588)126888256 |
| author_facet | Pšeničnyj, Boris N. 1937-2000 |
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| bvnumber | BV009943063 |
| classification_rvk | QH 421 SK 870 |
| classification_tum | MAT 916f MAT 912f |
| ctrlnum | (OCoLC)438724378 (DE-599)BVBBV009943063 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV009943063 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:43:39Z |
| institution | BVB |
| isbn | 3540570373 0387570373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006588159 |
| oclc_num | 438724378 |
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| physical | VIII, 147 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spelling | Pšeničnyj, Boris N. 1937-2000 Verfasser (DE-588)126888256 aut Metod linearizacii The linearization method for constrained optimization B. N. Pshenichnyj The linearization method for constraint optimization Berlin [u.a.] Springer 1994 VIII, 147 S. txt rdacontent n rdamedia nc rdacarrier Springer series in computational mathematics 22 Aus dem Russ. übers. Nebenbedingung (DE-588)4140066-5 gnd rswk-swf Linearisierung (DE-588)4199872-8 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Nebenbedingung (DE-588)4140066-5 s Linearisierung (DE-588)4199872-8 s DE-604 Springer series in computational mathematics 22 (DE-604)BV000012004 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006588159&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pšeničnyj, Boris N. 1937-2000 The linearization method for constrained optimization Springer series in computational mathematics Nebenbedingung (DE-588)4140066-5 gnd Linearisierung (DE-588)4199872-8 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4140066-5 (DE-588)4199872-8 (DE-588)4043664-0 |
| title | The linearization method for constrained optimization |
| title_alt | Metod linearizacii The linearization method for constraint optimization |
| title_auth | The linearization method for constrained optimization |
| title_exact_search | The linearization method for constrained optimization |
| title_full | The linearization method for constrained optimization B. N. Pshenichnyj |
| title_fullStr | The linearization method for constrained optimization B. N. Pshenichnyj |
| title_full_unstemmed | The linearization method for constrained optimization B. N. Pshenichnyj |
| title_short | The linearization method for constrained optimization |
| title_sort | the linearization method for constrained optimization |
| topic | Nebenbedingung (DE-588)4140066-5 gnd Linearisierung (DE-588)4199872-8 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Nebenbedingung Linearisierung Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006588159&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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