Constrained optimization and Lagrange multiplier methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, Massachusetts
Athena Scientific
1996
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| Series: | Athena scientific optimization and computation series
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 395 Seiten Diagramme |
| ISBN: | 1886529043 |
Staff View
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Record in the Search Index
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| adam_text | Contents Preface Chapter 1 xi Introduction 1.1 General Remarks 1.2 Notation and Mathematical Background 1.3 Unconstrained Minimization 1.3.1 Convergence Analysis of GradientMethods 1.3.2 Steepest Descent and Scaling 1.3.3 Newton’s Method and Its Modifications 1.3.4 Conjugate Direction and Conjugate Gradient Methods 1.3.5 Quasi-Newton Methods 1.3.6 Methods Not Requiring Evaluation of Derivatives 1.4 Constrained Minimization 1.5 Algorithms for Minimization Subject to Simple Constraints 1.6 Notes and Sources Chapter 2 1 6 18 20 39 40 49 59 65 66 76 93 The Method of Multipliers for Equality Constrained Problems 2.1 The Quadratic Penalty Function Method 2.2 The Original Method of Multipliers 2.2.1 Geometric Interpretation 2.2.2 Existence of Local Minima of the Augmented Lagrangian 2.2.3 The Primal Functional 2.2.4 Convergence Analysis 2.2.5 Comparison with the Penalty Method—Computational Aspects 2.3 Duality Framework for the Method of Multipliers 2.3.1 Stepsize Analysis for the Method of Multipliers 2.3.2 The Second-Order Multiplier Iteration 2.3.3 Quasi-Newton Versions of the Second-Order Iteration 2.3.4 Geometric Interpretation of the Second-Order Multiplier Iteration 96 104 105 107 113 115 121 125 126 133 138 139 vii
2.4 2.5 2.6 2.7 Multiplier Methods with Partial Elimination of Constraints Asymptotically Exact Minimization in Methods of Multipliers Primal-Dual Methods Not Utilizing a Penalty Function NotesandSources Chapter 3 , The Method of Multipliers for Inequality Constrained and Nondifferentiable Optimization Problems One-Sided Inequality Constraints Two-Sided Inequality Constraints Approximation Procedures for Nondifferentiable and Ill-Conditioned Optimization Problems 3.4 NotesandSources 3.1 3.2 3.3 Chapter 4 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 5.3 5.4 5.5 158 164 167 178 Exact Penalty Methods and Lagrangian Methods Nondifferentiable Exact Penalty Functions Linearization Algorithms Based on Nondifferentiable Exact Penalty Functions 4.2.1 Algorithms for Minimax Problems 4.2.2 Algorithms for Constrained Optimization Problems Differentiable Exact Penalty Functions 4.3.1 Exact Penalty Functions Depending on x and 2 4.3.2 Exact Penalty Functions Depending Only on x 4.3.3 Algorithms Based on Differentiable Exact Penalty Functions Lagrangian Methods—Local Convergence 4.4.1 First-Order Methods 4.4.2 Newton-like Methods for Equality Constraints 4.4.3 Newton-like Methods for Inequality Constraints 4.4.4 Quasi-Newton Versions Lagrangian Methods—Global Convergence 4.5.1 Combinations with Penalty and Multiplier Methods 4.5.2 Combinations with Differentiable Exact Penalty Methods— Newton and Quasi-Newton Versions 4.5.3 Combinations with Nondifferentiable Exact Penalty Methods— Powell’s Variable Metric Approach Notes and Sources Chapter 5 141 147 153 156 180 196 196 201 206 206 215 217 231 232 234
248 256 257 258 260 284 297 Nonquadratic Penalty Functions—Convex Programming Classes of Penalty Functions and Corresponding Methods of Multipliers 5.1.1 Penalty Functions for Equality Constraints 5.1.2 Penalty Functions for Inequality Constraints 5.1.3 Approximation Procedures Based on Nonquadratic Penalty Functions Convex Programming and Duality Convergence Analysis of Multiplier Methods Rate of Convergence Analysis Conditions for Penalty Methods to Be Exact 302 303 305 312 315 326 341 359
5.6 Large Scale Separable Integer Programming Problems and the Exponential Method of Multipliers 5.6.1 An Estimate of the Duality Gap 5.6.2 Solution of the Dual and Relaxed Problems 5.7 Notes and Sources 364 371 376 380 References 383 Index 393
|
| any_adam_object | 1 |
| author | Bertsekas, Dimitri P. 1942- |
| author_GND | (DE-588)171165519 |
| author_facet | Bertsekas, Dimitri P. 1942- |
| author_role | aut |
| author_sort | Bertsekas, Dimitri P. 1942- |
| author_variant | d p b dp dpb |
| building | Verbundindex |
| bvnumber | BV024974439 |
| classification_rvk | SK 870 |
| ctrlnum | (OCoLC)828164399 (DE-599)BVBBV024974439 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024974439 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:24:52Z |
| institution | BVB |
| isbn | 1886529043 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019641989 |
| oclc_num | 828164399 |
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| owner | DE-11 DE-739 |
| owner_facet | DE-11 DE-739 |
| physical | xiii, 395 Seiten Diagramme |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Athena Scientific |
| record_format | marc |
| series | Athena scientific optimization and computation series |
| series2 | Athena scientific optimization and computation series |
| spelling | Bertsekas, Dimitri P. 1942- Verfasser (DE-588)171165519 aut Constrained optimization and Lagrange multiplier methods Dimitri P. Bertsekas Belmont, Massachusetts Athena Scientific 1996 xiii, 395 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Athena scientific optimization and computation series 4 Optimierung (DE-588)4043664-0 gnd rswk-swf Lagrange-Multiplikator (DE-588)4401279-2 gnd rswk-swf Nebenbedingung (DE-588)4140066-5 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Optimierung (DE-588)4043664-0 s Nebenbedingung (DE-588)4140066-5 s Lagrange-Multiplikator (DE-588)4401279-2 s DE-604 Mathematik (DE-588)4037944-9 s 1\p DE-604 Athena scientific optimization and computation series 4 (DE-604)BV015264203 4 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bertsekas, Dimitri P. 1942- Constrained optimization and Lagrange multiplier methods Athena scientific optimization and computation series Optimierung (DE-588)4043664-0 gnd Lagrange-Multiplikator (DE-588)4401279-2 gnd Nebenbedingung (DE-588)4140066-5 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4401279-2 (DE-588)4140066-5 (DE-588)4037944-9 |
| title | Constrained optimization and Lagrange multiplier methods |
| title_auth | Constrained optimization and Lagrange multiplier methods |
| title_exact_search | Constrained optimization and Lagrange multiplier methods |
| title_full | Constrained optimization and Lagrange multiplier methods Dimitri P. Bertsekas |
| title_fullStr | Constrained optimization and Lagrange multiplier methods Dimitri P. Bertsekas |
| title_full_unstemmed | Constrained optimization and Lagrange multiplier methods Dimitri P. Bertsekas |
| title_short | Constrained optimization and Lagrange multiplier methods |
| title_sort | constrained optimization and lagrange multiplier methods |
| topic | Optimierung (DE-588)4043664-0 gnd Lagrange-Multiplikator (DE-588)4401279-2 gnd Nebenbedingung (DE-588)4140066-5 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Optimierung Lagrange-Multiplikator Nebenbedingung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641989&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT bertsekasdimitrip constrainedoptimizationandlagrangemultipliermethods |