Conjugate gradient algorithms in nonconvex optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2009
|
| Series: | Nonconvex optimization and its applications
89 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783540856344 |
Staff View
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Record in the Search Index
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| adam_text | 3.1 INTRODUCTION 109 CONTENTS CONJUGATE DIRECTION METHODS FOR QUADRATIC
PROBLEMS 1 1.1 INTRODUCTION 1 1.2 CONJUGATE DIRECTION METHODS 4 1.3
CONJUGATE GRADIENT ERROR ALGORITHMS 13 1.4 CONJUGATE GRADIENT RESIDUAL
ALGORITHMS 21 1.5 THE METHOD OF SHORTEST RESIDUAIS 26 1.6 RATE OF
CONVERGENCE 28 1.7 RELATIONS WITH A DIRECT SOLVER FOR A SET OF LINEAR
EQUATIONS 38 1.8 LIMITED MEMORY QUASI-NEWTON ALGORITHMS 45 1.9
REDUCED-HESSIAN QUASI-NEWTON ALGORITHMS 53 1.10 LIMITED MEMORY
REDUCED-HESSIAN QUASI-NEWTON ALGORITHMS 56 1.11 CONJUGATE NON-GRADIENT
ALGORITHM 59 1.12 NOTES 61 CONJUGATE GRADIENT METHODS FOR NONCONVEX
PROBLEMS 63 2.1 INTRODUCTION 63 2.2 LINE SEARCH METHODS 65 2.3 GENERAL
CONVERGENCE RESULTS 70 2.4 MORE-THUENTE STEP-LENGTH SELECTION ALGORITHM
76 2.5 HAGER-ZHANG STEP-LENGTH SELECTION ALGORITHM 80 2.6 NONLINEAR
CONJUGATE GRADIENT ALGORITHMS 84 2.7 GLOBAL CONVERGENCE OF THE
FLETCHER-REEVES ALGORITHM 87 2.8 OTHER VERSIONS OF THE FLETCHER-REEVES
ALGORITHM 96 2.9 GLOBAL CONVERGENCE OF THE POLAK-RIBIERE ALGORITHM 98
2.10 HESTENES-STIEFEL VERSIONS OF THE STANDARD CONJUGATE GRADIENT
ALGORITHM 101 2.11 NOTES 106 MEMORYLESS QUASI-NEWTON METHODS 109
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/990020193 DIGITALISIERT
DURCH XIV CONTENTS 3.2 CONJUGATE GRADIENT ALGORITHM AS THE MEMORYLESS
QUASI-NEWTON METHOD 1 12 3.3 BEALE S RESTART RULE 116 3.4 CONVERGENCE OF
THE SHANNO ALGORITHM 118 3.5 NOTES 127 4 PRECONDITIONED CONJUGATE
GRADIENT ALGORITHMS 133 4.1 INTRODUCTION 133 4.2 RATES OF CONVERGENCE
134 4.3 CONJUGATE GRADIENT ALGORITHM AND THE NEWTON METHOD 139 4.4
GENERIC PRECONDITIONED CONJUGATE GRADIENT ALGORITHM 145 4.5
QUASI-NEWTON-LIKE VARIABLE STORAGE CONJUGATE GRADIENT ALGORITHM 148 4.6
SCALING THE IDENTITY 155 4.7 NOTES 158 5 LIMITED MEMORY QUASI-NEWTON
ALGORITHMS 159 5.1 INTRODUCTION 159 5.2 GLOBAL CONVERGENCE OF THE
LIMITED MEMORY BFGS ALGORITHM 163 5.3 COMPACT REPRESENTATION OF THE BFGS
APPROXIMATION OF THE INVERSE HESSIAN MATRIX 169 5.4 THE COMPACT
REPRESENTATION OF THE BFGS APPROXIMATION OF THE HESSIAN MATRIX 175 5.5
NUMERICAL EXPERIMENTS 178 5.6 NOTES 186 6 THE METHOD OF SHORTEST
RESIDUAIS AND NONDIFFERENTIABLE OPTIMIZATION 191 6.1 INTRODUCTION 191
6.2 THE METHOD OF CONJUGATE SUBGRADIENT BY LEMARECHAL AND WOLFE .. 192
6.3 CONJUGATE SUBGRADIENT ALGORITHM FOR PROBLEMS WITH SEMISMOOTH
FUNCTIONS 204 6.4 SUBGRADIENT ALGORITHMS WITH FINITE STORAGE 210 6.5
NOTES 215 7 TH CONTENTS XV 7.9 NUMERICAL EXPERIMENTS: COMPARISON TO THE
MEMORYLESS QUASI-NEWTON METHOD 256 7.10 NUMERICA] EXPERIMENTS:
COMPARISON TO THE LIMITED MEMORY QUASI-NEWTON METHOD 257 7.11 NUMERICAL
EXPERIMENTS: COMPARISON TO THE HAGER-ZHANG ALGORITHM 264 7.12 NOTES 267
8 THE PRECONDITIONED SHORTEST RESIDUAIS ALGORITHM 279 8.1 INTRODUCTION
279 8.2 GENERAL PRECONDITIONED METHOD OF SHORTEST RESIDUAIS 281 8.3
GLOBALLY CONVERGENT PRECONDITIONED CONJUGATE GRADIENT ALGORITHM 286 8.4
SCALING MATRICES 288 8.5 CONJUGATE GRADIENT ALGORITHM WITH THE BFGS
SCALING MATRICES ...291 8.6 NUMERICAL EXPERIMENTS 293 8.7 NOTES 297 9
OPTIMIZATION ON A POLYHEDRON 299 9.1 INTRODUCTION 299 9.2 EXPOSED SETS
308 9.3 THE IDENTIFICATION OF ACTIVE CONSTRAINTS 310 9.4 GRADIENT
PROJECTION METHOD 313 9.5 ON THE STOPPING CRITERION 319 9.6 NOTES 324 10
CONJUGATE GRADIENT ALGORITHMS FOR PROBLEMS WITH BOX CONSTRAINTS . 327
10.1 INTRODUCTION 327 10.2 GENERAL CONVERGENCE THEORY 328 10.3 THE
GLOBALLY CONVERGENT POLAK-RIBIERE VERSION OF ALGORITHM 10.1 342 10.4
CONVERGENCE ANALYSIS OF THE FLETCHER-REEVES VERSION OF ALGORITHM 10.1
350 10.5 NUMERICAL EXPERIMENTS 357 10.6 NOTES 359 11 PRECONDITIONED
CONJUGATE GRADIENT ALGORITHMS FOR PROBLEMS WIT 473 XVI CONTENTS 11.7
ALGORITHM 11.1 AND ALGORITHM 11.2 APPLIED TO PROBLEMS WITH STRONGLY
CONVEX FUNCTIONS 389 11.8 NUMERICAL EXPERIMENTS 390 11.9 NOTES 391 12
PRECONDITIONED CONJUGATE GRADIENT BASED REDUCED-HESSIAN METHODS 399 12.1
INTRODUCTION 399 12.2 BFGS UPDATE WITH COLUMN SCALING 400 12.3 THE
PRECONDITIONED METHOD OF SHORTEST RESIDUAIS WITH COLUMN SCALING 409 12.4
REDUCED-HESSIAN QUASI-NEWTON ALGORITHMS 412 12.5 LIMITED MEMORY
REDUCED-HESSIAN QUASI-NEWTON ALGORITHMS 420 12.6 PRECONDITIONED
CONJUGATE GRADIENT BASED REDUCED-HESSIAN ALGORITHM 424 12.7 NOTES 428 A
ELEMENTS OF TOPOLOGY AND ANALYSIS 429 A. 1 THE TOPOLOGY OF THE EUCLIDEAN
SPACE 429 A.2 CONTINUITY AND CONVEXITY 432 A.3 DERIVATIVES 435 B
ELEMENTS OF LINEAR ALGEBRA 441 B. 1 VECTOR AND MATRIX NORMS 441 B.2
SPECTRAL DECOMPOSITION 442 B.3 DETERMINANT AND TRACE 447 C ELEMENTS OF
NUMERICAL LINEAR ALGEBRA 449 C.L CONDITION NUMBER AND LINEAR EQUATIONS
449 C.2 THE LU AND CHOLESKY FACTORIZATIONS 450 C.3 THE QR FACTORIZATION
452 C.4 HOUSEHOLDER QR 454 C.5 GIVENS QR 456 C.6 GRAM-SCHMIDT QR 459
REFERENCES 463 INDEX
|
| any_adam_object | 1 |
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| author_facet | Pytlak, Radoslaw |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| language | English |
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| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Springer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Pytlak, Radoslaw Verfasser aut Conjugate gradient algorithms in nonconvex optimization Radoslaw Pytlak Berlin [u.a.] Springer 2009 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Nonconvex optimization and its applications 89 Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 s Konjugierte-Gradienten-Methode (DE-588)4255670-3 s DE-604 Erscheint auch als Druckausgabe 978-3-540-85633-7 Nonconvex optimization and its applications 89 (DE-604)BV036654736 89 http://springerlink.com/content/j5j313/?p=0ae8aedb367d4f9aaf76ab9e91c8b9ca&pi=0 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017467733&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pytlak, Radoslaw Conjugate gradient algorithms in nonconvex optimization Nonconvex optimization and its applications Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| subject_GND | (DE-588)4255670-3 (DE-588)4309215-9 |
| title | Conjugate gradient algorithms in nonconvex optimization |
| title_auth | Conjugate gradient algorithms in nonconvex optimization |
| title_exact_search | Conjugate gradient algorithms in nonconvex optimization |
| title_full | Conjugate gradient algorithms in nonconvex optimization Radoslaw Pytlak |
| title_fullStr | Conjugate gradient algorithms in nonconvex optimization Radoslaw Pytlak |
| title_full_unstemmed | Conjugate gradient algorithms in nonconvex optimization Radoslaw Pytlak |
| title_short | Conjugate gradient algorithms in nonconvex optimization |
| title_sort | conjugate gradient algorithms in nonconvex optimization |
| topic | Konjugierte-Gradienten-Methode (DE-588)4255670-3 gnd Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| topic_facet | Konjugierte-Gradienten-Methode Nichtkonvexe Optimierung |
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