Introduction to derivative-free optimization:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia
Society for Industrial and Applied Mathematics [u.a.]
2009
|
| Schriftenreihe: | MPS-SIAM series on optimization
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 277 Seiten graph. Darst. |
| ISBN: | 9780898716689 |
Internformat
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Datensatz im Suchindex
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| adam_text | INTRODUCTION TO DERIVATIVE-FREE OPTIMIZATION SLAM. ANDREW R. CONN KATYA
SCHEINBERG IBM YORKTOWN HEIGHTS, NEW YORK LUIS N. VICENTE UNIVERSIDADE
DE COIMBRA COIMBRA, PORTUGAL MOS SOCIETY FOR INDUSTRIAL AND APPLIED
MATHEMATICS MATHEMATICAL PROGRAMMING SOCIETY PHILADELPHIA PHILADELPHIA
CONTENTS PREFACE XI 1 INTRODUCTION 1 1.1 WHY DERIVATIVE-FREE
OPTIMIZATION 1 1.2 EXAMPLES OF PROBLEMS WHERE DERIVATIVES ARE
UNAVAILABLE 3 1.3 LIMITATIONS OF DERIVATIVE-FREE OPTIMIZATION 5 1.4 HOW
DERIVATIVE-FREE ALGORITHMS SHOULD WORK 7 1.5 A SHORT SUMMARY OF THE BOOK
11 1 SAMPLING AND MODELING 13 2 SAMPLING AND LINEAR MODELS 15 2.1
POSITIVE SPANNING SETS AND POSITIVE BASES 15 2.2 GRADIENT ESTIMATES USED
IN DIRECT SEARCH 21 2.3 LINEAR INTERPOLATION AND REGRESSION MODELS 24
2.4 ERROR BOUNDS FOR LINEAR INTERPOLATION AND REGRESSION 26 2.5 OTHER
GEOMETRICAL CONCEPTS 29 2.6 SIMPLEX GRADIENTS 32 2.7 EXERCISES 33 3
INTERPOLATING NONLINEAR MODELS 35 3.1 BASIC CONCEPTS IN INTERPOLATION 36
3.2 LAGRANGE POLYNOMIALS 39 3.3 *-POISEDNESS AND OTHER MEASURES OF WELL
POISEDNESS 42 3.4 CONDITION NUMBER AS A MEASURE OF WELL POISEDNESS 48
3.5 EXERCISES 56 4 REGRESSION NONLINEAR MODELS 57 4.1 BASIC CONCEPTS IN
POLYNOMIAL LEAST-SQUARES REGRESSION 58 4.2 LAGRANGE POLYNOMIALS IN THE
REGRESSION SENSE 60 4.3 *-POISEDNESS IN THE REGRESSION SENSE 62 4.4
CONDITION NUMBER AS A MEASURE OF WELL POISEDNESS 68 4.5 NOTES AND
REFERENCES 70 4.6 EXERCISES 72 VII VIII CONTENTS UNDERDETERMINED
INTERPOLATING MODELS 73 5.1 THE CHOICE OF AN UNDERDETERMINED MODEL 74
5.2 LAGRANGE POLYNOMIALS AND *-POISEDNESS FOR UNDERDETERMINED INTER
POLATION 76 5.3 MINIMUM FROBENIUS NORM MODELS 80 5.4 NOTES AND
REFERENCES 87 5.5 EXERCISES 87 ENSURING WELL POISEDNESS AND SUITABLE
DERIVATIVE-FREE MODELS 89 6.1 FULLY LINEAR AND FULLY QUADRATIC MODELS 90
6.2 ENSURING WELL POISEDNESS USING LAGRANGE POLYNOMIALS 93 6.3 ENSURING
WELL POISEDNESS USING PIVOTAL ALGORITHMS 99 6.4 PRACTICAL CONSIDERATIONS
OF GEOMETRY IMPROVEMENT ALGORITHMS 107 6.5 ENSURING WELL POISEDNESS FOR
REGRESSION AND MINIMUM FROBENIUS NORM MODELS 108 6.6 OTHER NOTES AND
REFERENCES 110 6.7 EXERCISES 112 II FRAMEWORKS AND ALGORITHMS 113 7
DIRECTIONAL DIRECT-SEARCH METHODS 115 7.1 THE COORDINATE-SEARCH METHOD
115 7.2 A DIRECTIONAL DIRECT-SEARCH FRAMEWORK 118 7.3 GLOBAL CONVERGENCE
IN THE CONTINUOUSLY DIFFERENTIABLE CASE 120 7.4 GLOBAL CONVERGENCE IN
THE NONSMOOTH CASE 124 7.5 SIMPLE DECREASE WITH INTEGER LATTICES 127 7.6
THE MESH ADAPTIVE DIRECT-SEARCH METHOD 132 7.7 IMPOSING SUFFICIENT
DECREASE 134 7.8 OTHER NOTES AND REFERENCES 135 7.9 EXERCISES 139 8
SIMPLICIAL DIRECT-SEARCH METHODS 141 8.1 THE NELDER-MEAD SIMPLEX METHOD
141 8.2 PROPERTIES OF THE NELDER-MEAD SIMPLEX METHOD 148 8.3 A GLOBALLY
CONVERGENT VARIANT OF THE NELDER-MEAD METHOD 149 8.4 OTHER NOTES AND
REFERENCES 161 8.5 EXERCISES 161 9 LINE-SEARCH METHODS BASED ON SIMPLEX
DERIVATIVES 163 9.1 A LINE-SEARCH FRAMEWORK 163 9.2 GLOBAL CONVERGENCE
FOR FIRST-ORDER CRITICAL POINTS 165 9.3 ANALYSIS FOR NOISE 167 9.4 THE
IMPLICIT-FILTERING ALGORITHM 168 9.5 OTHER SIMPLEX DERIVATIVES 169 9.6
OTHER NOTES AND REFERENCES 170 9.7 EXERCISES 171 CONTENTS IX 10
TRUST-REGION METHODS BASED ON DERIVATIVE-FREE MODELS 173 10.1 THE
TRUST-REGION FRAMEWORK BASICS 173 10.2 CONDITIONS ON THE TRUST-REGION
MODELS 179 10.3 DERIVATIVE-FREE TRUST-REGION METHODS (FIRST ORDER) 181
10.4 GLOBAL CONVERGENCE FOR FIRST-ORDER CRITICAL POINTS 185 10.5
DERIVATIVE-FREE TRUST-REGION METHODS (SECOND ORDER) 191 10.6 GLOBAL
CONVERGENCE FOR SECOND-ORDER CRITICAL POINTS 194 10.7 MODEL ACCURACY IN
LARGER CONCENTRIC BALLS 200 10.8 TRUST-REGION SUBPROBLEM 202 10.9 OTHER
NOTES AND REFERENCES 204 10.10 EXERCISES 205 11 TRUST-REGION
INTERPOLATION-BASED METHODS 207 11.1 COMMON FEATURES AND CONSIDERATIONS
207 11.2 THE DFO APPROACH 208 11.3 POWELL S METHODS 211 11.4 WEDGE
METHODS 215 11.5 OTHER NOTES AND REFERENCES 225 III REVIEW OF OTHER
TOPICS 227 12 REVIEW OF SURROGATE MODEL MANAGEMENT 229 12.1 SURROGATE
MODELING 229 12.2 RIGOROUS OPTIMIZATION FRAMEWORKS TO HANDLE SURROGATE
MODELS . . . .235 12.3 EXERCISES 240 13 REVIEW OF CONSTRAINED AND OTHER
EXTENSIONS TO DERIVATIVE-FREE OPTIMIZATION 241 13.1 DIRECTIONAL
DIRECT-SEARCH METHODS 242 13.2 TRUST-REGION INTERPOLATION-BASED METHODS
248 13.3 DERIVATIVE-FREE APPROACHES FOR GLOBAL OPTIMIZATION,
MIXED-INTEGER PROGRAMMING, AND OTHER PROBLEMS 249 APPENDIX SOFTWARE FOR
DERIVATIVE-FREE OPTIMIZATION 251 BIBLIOGRAPHY 255 INDEX 271
|
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| language | English |
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| spelling | Conn, Andrew R. Verfasser aut Introduction to derivative-free optimization Andrew R. Conn ; Katya Scheinberg ; Luis N. Vicente Philadelphia Society for Industrial and Applied Mathematics [u.a.] 2009 XII, 277 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier MPS-SIAM series on optimization 8 Includes bibliographical references and index Mathematik Mathematisches Modell Mathematical models Mathematical optimization Industrial applications Engineering mathematics Industrial engineering Mathematics Search theory Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Simplexverfahren (DE-588)4181488-5 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s DE-604 Simplexverfahren (DE-588)4181488-5 s Nichtlineare Optimierung (DE-588)4128192-5 s Scheinberg, Katya Verfasser (DE-588)137333021 aut Vicente, Luís N. Verfasser aut MPS-SIAM series on optimization 8 (DE-604)BV023088428 8 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017109790&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conn, Andrew R. Scheinberg, Katya Vicente, Luís N. Introduction to derivative-free optimization MPS-SIAM series on optimization Mathematik Mathematisches Modell Mathematical models Mathematical optimization Industrial applications Engineering mathematics Industrial engineering Mathematics Search theory Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Simplexverfahren (DE-588)4181488-5 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4114528-8 (DE-588)4181488-5 |
| title | Introduction to derivative-free optimization |
| title_auth | Introduction to derivative-free optimization |
| title_exact_search | Introduction to derivative-free optimization |
| title_full | Introduction to derivative-free optimization Andrew R. Conn ; Katya Scheinberg ; Luis N. Vicente |
| title_fullStr | Introduction to derivative-free optimization Andrew R. Conn ; Katya Scheinberg ; Luis N. Vicente |
| title_full_unstemmed | Introduction to derivative-free optimization Andrew R. Conn ; Katya Scheinberg ; Luis N. Vicente |
| title_short | Introduction to derivative-free optimization |
| title_sort | introduction to derivative free optimization |
| topic | Mathematik Mathematisches Modell Mathematical models Mathematical optimization Industrial applications Engineering mathematics Industrial engineering Mathematics Search theory Nonlinear theories Nichtlineare Optimierung (DE-588)4128192-5 gnd Mathematisches Modell (DE-588)4114528-8 gnd Simplexverfahren (DE-588)4181488-5 gnd |
| topic_facet | Mathematik Mathematisches Modell Mathematical models Mathematical optimization Industrial applications Engineering mathematics Industrial engineering Mathematics Search theory Nonlinear theories Nichtlineare Optimierung Simplexverfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017109790&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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