Nonlinear optimization with engineering applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
2008
|
| Edition: | 1. ed. |
| Series: | Springer optimization and its applications
19 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 280 S. Ill., graph. Darst. |
| ISBN: | 9780387787220 |
Staff View
MARC
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Record in the Search Index
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| adam_text | NONLINEAR OPTIMIZATION WITH ENGINEERING APPLICATIONS BY MICHAEL
BARTHOLOMEW-BIGGS UNIVERSITY OF HERTFORDSHIRE, UK VA SPRINGER CONTENTS
PREFACE XI LIST OF FIGURES XIII LIST OF TABLES XV 1. INTRODUCING
OPTIMIZATION 1 1.1 A TANK DESIGN PROBLEM 1 1.2 LEAST SQUARES
DATA-FITTING 3 1.3 A ROUTING PROBLEM 7 2. ONE-VARIABLE OPTIMIZATION 11
2.1 OPTIMALITY CONDITIONS 11 2.2 THE BISECTION METHOD 12 2.3 THE SECANT
METHOD 16 2.4 THE NEWTON METHOD 18 2.5 SAMPLE APPLICATIONS AND RESULTS
24 3. APPLICATIONS IN N VARIABLES 33 3.1 DATA-FITTING PROBLEMS 33 3.2
THE ROUTING PROBLEM 36 3.3 AN OPTIMAL CONTROL PROBLEM 38 4. N- VARIABLE
UNCONSTRAINED OPTIMIZATION 41 4.1 OPTIMALITY CONDITIONS 41 4.2
VISUALISING PROBLEMS IN SEVERAL VARIABLES 43 4.3 OPTIMIZATION SOFTWARE
AND TEST PROBLEMS 45 5. DIRECT SEARCH METHODS 53 5.1 UNIVARIATE SEARCH
53 VI CONTENTS 5.2 THE NELDER AND MEAD SIMPLEX METHOD 55 5.3 DIRECT 58
5.4 RESULTS WITH DIRECT SEARCH METHODS 60 6. COMPUTING DERIVATIVES 63
6.1 HAND-CRAFTED DERIVATIVES 63 6.2 FINITE DIFFERENCE ESTIMATES OF
DERIVATIVES 66 6.3 AUTOMATIC DIFFERENTIATION 68 6.4 COMPUTATIONAL COSTS
OF DERIVATIVES 72 7. THE STEEPEST DESCENT METHOD 75 7.1 INTRODUCTION 75
7.2 LINE SEARCHES 76 7.3 CONVERGENCE OF THE STEEPEST DESCENT METHOD 78
7.4 RESULTS WITH STEEPEST DESCENT 81 8. WEAK LINE SEARCHES AND
CONVERGENCE 83 8.1 WOLFE S CONVERGENCE THEOREM 83 8.2 THE ARMIJO LINE
SEARCH 86 8.3 FURTHER RESULTS WITH STEEPEST DESCENT 87 9. NEWTON AND
NEWTON-LIKE METHODS 91 9.1 QUADRATIC MODELS AND THE NEWTON STEP 91 9.2
NEWTON METHOD ADVANTAGES AND DRAWBACKS 96 9.3 SEARCH DIRECTIONS FROM
INDEFINITE HESSIANS 97 9.4 RESULTS WITH THE NEWTON METHOD 100 9.5 THE
GAUSS-NEWTON METHOD 103 9.6 RESULTS WITH THE GAUSS-NEWTON METHOD 105 10.
QUASI-NEWTON METHODS 107 10.1 APPROXIMATE SECOND-DERIVATIVE INFORMATION
107 10.2 RANK-TWO UPDATES FOR THE INVERSE HESSIAN 108 10.3 CONVERGENCE
OF QUASI-NEWTON METHODS 112 10.4 RESULTS WITH QUASI-NEWTON METHODS 113
10.5 SOME FURTHER UPDATING FORMULAE { 115 11. CONJUGATE GRADIENT METHODS
119 11.1 CONJUGATE GRADIENTS FOR A QUADRATIC Q(X) 119 11.2 CONJUGATE
GRADIENTS AND GENERAL FUNCTIONS 124 CONTENTS VII 11.3 CONVERGENCE OF
CONJUGATE GRADIENT METHODS 126 11.4 RESULTS WITH CONJUGATE GRADIENTS 127
11.5 THE TRUNCATED NEWTON METHOD 129 12. A SUMMARY OF UNCONSTRAINED
METHODS 131 13. OPTIMIZATION WITH RESTRICTIONS 133 13.1 EXCLUDING
NEGATIVE VARIABLES 133 13.2 THE PREVENTIVE MAINTENANCE PROBLEM 135 14.
LARGER-SCALE PROBLEMS 141 14.1 CONTROL PROBLEMS WITH MANY TIME STEPS 141
14.2 OVERHEAD COSTS AND RUNTIMES 143 15. GLOBAL UNCONSTRAINED
OPTIMIZATION 147 15.1 MULTISTART METHODS 148 15.2 GLOBAL SOLUTION OF
ROUTING PROBLEMS 149 15.3 GLOBAL SOLUTION OF A FEED-BLENDING PROBLEM 150
15.4 GLOBAL SOLUTION OF A SENSITIVITY PROBLEM 153 16. EQUALITY
CONSTRAINED OPTIMIZATION 155 16.1 PROBLEMS WITH EQUALITY CONSTRAINTS 155
16.2 OPTIMALITY CONDITIONS 158 16.3 A WORKED EXAMPLE 161 16.4
INTERPRETATION OF LAGRANGE MULTIPLIERS 162 16.5 SOME EXAMPLE PROBLEMS
164 17. LINEAR EQUALITY CONSTRAINTS 169 17.1 QUADRATIC PROGRAMMING 169
17.2 SAMPLE EQP SOLUTIONS 170 17.3 REDUCED-GRADIENT METHODS 172 17.4
RESULTS WITH A REDUCED-GRADIENT METHOD 179 17.5 PROJECTED-GRADIENT
METHODS 180 18. PENALTY FUNCTION METHODS 183 18.1 INTRODUCTION / 183
18.2 PENALTY FUNCTIONS 185 18.3 THE AUGMENTED LAGRANGIAN 189 18.4
RESULTS WITH P-SUMT AND AL-SUMT 192 VIII CONTENTS 18.5 EXACT PENALTY
FUNCTIONS 195 19. SEQUENTIAL QUADRATIC PROGRAMMING 197 19.1
QUADRATIC/LINEAR MODELS 197 19.2 SQP METHODS BASED ON PENALTY FUNCTIONS
200 19.3 RESULTS WITH AL-SQP 205 19.4 SQP LINE SEARCHES AND THE MARATOS
EFFECT 208 20. INEQUALITY CONSTRAINED OPTIMIZATION 211 20.1 PROBLEMS
WITH INEQUALITY CONSTRAINTS 211 20.2 OPTIMALITY CONDITIONS 216 20.3
TRANSFORMING INEQUALITIES TO EQUALITIES 220 20.4 TRANSFORMING
INEQUALITIES TO SIMPLE BOUNDS 221 20.5 EXAMPLE PROBLEMS 221 21.
EXTENDING EQUALITY CONSTRAINT METHODS 225 21.1 QUADRATIC PROGRAMMING
WITH INEQUALITIES 225 21.2 REDUCED-GRADIENTS FOR INEQUALITY CONSTRAINTS
229 21.3 PENALTY FUNCTIONS FOR INEQUALITY CONSTRAINTS 231 21.4 AL-SUMT
FOR INEQUALITY CONSTRAINTS 233 21.5 SQP FOR INEQUALITY CONSTRAINTS 234
21.6 RESULTS WITH P-SUMT, AL-SUMT AND AL-SQP 235 22. BARRIER FUNCTION
METHODS 239 22.1 PROBLEMS WITH INEQUALITY CONSTRAINTS ONLY 239 22.2
BARRIER FUNCTIONS 241 22.3 RESULTS WITH B-SUMT 244 23. INTERIOR POINT
METHODS 249 23.1 FORMING THE TRANSFORMED PROBLEM B-NLP 249 23.2
APPROXIMATE SOLUTIONS OF PROBLEM B-NLP 250 23.3 AN INTERIOR POINT
ALGORITHM 254 23.4 RESULTS WITH IPM 256 24. A SUMMARY OF CONSTRAINED
METHOD^ 259 25. THE OPTIMA SOFTWARE 261 25.1 ACCESSING OPTIMA 261 25.2
RUNNING OPTIMA 262 CONTENTS IX 25.3 MODIFYING AND CREATING TEST PROBLEMS
262 25.4 MODIFYING OPTIMIZATION METHODS 271 REFERENCES 273 INDEX 27 7
|
| adam_txt |
NONLINEAR OPTIMIZATION WITH ENGINEERING APPLICATIONS BY MICHAEL
BARTHOLOMEW-BIGGS UNIVERSITY OF HERTFORDSHIRE, UK VA SPRINGER CONTENTS
PREFACE XI LIST OF FIGURES XIII LIST OF TABLES XV 1. INTRODUCING
OPTIMIZATION 1 1.1 A TANK DESIGN PROBLEM 1 1.2 LEAST SQUARES
DATA-FITTING 3 1.3 A ROUTING PROBLEM 7 2. ONE-VARIABLE OPTIMIZATION 11
2.1 OPTIMALITY CONDITIONS 11 2.2 THE BISECTION METHOD 12 2.3 THE SECANT
METHOD 16 2.4 THE NEWTON METHOD 18 2.5 SAMPLE APPLICATIONS AND RESULTS
24 3. APPLICATIONS IN N VARIABLES 33 3.1 DATA-FITTING PROBLEMS 33 3.2
THE ROUTING PROBLEM 36 3.3 AN OPTIMAL CONTROL PROBLEM 38 4. N- VARIABLE
UNCONSTRAINED OPTIMIZATION 41 4.1 OPTIMALITY CONDITIONS 41 4.2
VISUALISING PROBLEMS IN SEVERAL VARIABLES 43 4.3 OPTIMIZATION SOFTWARE
AND TEST PROBLEMS 45 5. DIRECT SEARCH METHODS 53 5.1 UNIVARIATE SEARCH
53 VI CONTENTS 5.2 THE NELDER AND MEAD SIMPLEX METHOD 55 5.3 DIRECT 58
5.4 RESULTS WITH DIRECT SEARCH METHODS 60 6. COMPUTING DERIVATIVES 63
6.1 HAND-CRAFTED DERIVATIVES 63 6.2 FINITE DIFFERENCE ESTIMATES OF
DERIVATIVES 66 6.3 AUTOMATIC DIFFERENTIATION 68 6.4 COMPUTATIONAL COSTS
OF DERIVATIVES 72 7. THE STEEPEST DESCENT METHOD 75 7.1 INTRODUCTION 75
7.2 LINE SEARCHES 76 7.3 CONVERGENCE OF THE STEEPEST DESCENT METHOD 78
7.4 RESULTS WITH STEEPEST DESCENT 81 8. WEAK LINE SEARCHES AND
CONVERGENCE 83 8.1 WOLFE'S CONVERGENCE THEOREM 83 8.2 THE ARMIJO LINE
SEARCH 86 8.3 FURTHER RESULTS WITH STEEPEST DESCENT 87 9. NEWTON AND
NEWTON-LIKE METHODS 91 9.1 QUADRATIC MODELS AND THE NEWTON STEP 91 9.2
NEWTON METHOD ADVANTAGES AND DRAWBACKS 96 9.3 SEARCH DIRECTIONS FROM
INDEFINITE HESSIANS 97 9.4 RESULTS WITH THE NEWTON METHOD 100 9.5 THE
GAUSS-NEWTON METHOD 103 9.6 RESULTS WITH THE GAUSS-NEWTON METHOD 105 10.
QUASI-NEWTON METHODS 107 10.1 APPROXIMATE SECOND-DERIVATIVE INFORMATION
107 10.2 RANK-TWO UPDATES FOR THE INVERSE HESSIAN 108 10.3 CONVERGENCE
OF QUASI-NEWTON METHODS 112 10.4 RESULTS WITH QUASI-NEWTON METHODS 113
10.5 SOME FURTHER UPDATING FORMULAE { 115 11. CONJUGATE GRADIENT METHODS
119 11.1 CONJUGATE GRADIENTS FOR A QUADRATIC Q(X) 119 11.2 CONJUGATE
GRADIENTS AND GENERAL FUNCTIONS 124 CONTENTS VII 11.3 CONVERGENCE OF
CONJUGATE GRADIENT METHODS 126 11.4 RESULTS WITH CONJUGATE GRADIENTS 127
11.5 THE TRUNCATED NEWTON METHOD 129 12. A SUMMARY OF UNCONSTRAINED
METHODS 131 13. OPTIMIZATION WITH RESTRICTIONS 133 13.1 EXCLUDING
NEGATIVE VARIABLES 133 13.2 THE PREVENTIVE MAINTENANCE PROBLEM 135 14.
LARGER-SCALE PROBLEMS 141 14.1 CONTROL PROBLEMS WITH MANY TIME STEPS 141
14.2 OVERHEAD COSTS AND RUNTIMES 143 15. GLOBAL UNCONSTRAINED
OPTIMIZATION 147 15.1 MULTISTART METHODS 148 15.2 GLOBAL SOLUTION OF
ROUTING PROBLEMS 149 15.3 GLOBAL SOLUTION OF A FEED-BLENDING PROBLEM 150
15.4 GLOBAL SOLUTION OF A SENSITIVITY PROBLEM 153 16. EQUALITY
CONSTRAINED OPTIMIZATION 155 16.1 PROBLEMS WITH EQUALITY CONSTRAINTS 155
16.2 OPTIMALITY CONDITIONS 158 16.3 A WORKED EXAMPLE 161 16.4
INTERPRETATION OF LAGRANGE MULTIPLIERS 162 16.5 SOME EXAMPLE PROBLEMS
164 17. LINEAR EQUALITY CONSTRAINTS 169 17.1 QUADRATIC PROGRAMMING 169
17.2 SAMPLE EQP SOLUTIONS 170 17.3 REDUCED-GRADIENT METHODS 172 17.4
RESULTS WITH A REDUCED-GRADIENT METHOD 179 17.5 PROJECTED-GRADIENT
METHODS 180 18. PENALTY FUNCTION METHODS 183 18.1 INTRODUCTION / 183
18.2 PENALTY FUNCTIONS 185 18.3 THE AUGMENTED LAGRANGIAN 189 18.4
RESULTS WITH P-SUMT AND AL-SUMT 192 VIII CONTENTS 18.5 EXACT PENALTY
FUNCTIONS 195 19. SEQUENTIAL QUADRATIC PROGRAMMING 197 19.1
QUADRATIC/LINEAR MODELS 197 19.2 SQP METHODS BASED ON PENALTY FUNCTIONS
200 19.3 RESULTS WITH AL-SQP 205 19.4 SQP LINE SEARCHES AND THE MARATOS
EFFECT 208 20. INEQUALITY CONSTRAINED OPTIMIZATION 211 20.1 PROBLEMS
WITH INEQUALITY CONSTRAINTS 211 20.2 OPTIMALITY CONDITIONS 216 20.3
TRANSFORMING INEQUALITIES TO EQUALITIES 220 20.4 TRANSFORMING
INEQUALITIES TO SIMPLE BOUNDS 221 20.5 EXAMPLE PROBLEMS 221 21.
EXTENDING EQUALITY CONSTRAINT METHODS 225 21.1 QUADRATIC PROGRAMMING
WITH INEQUALITIES 225 21.2 REDUCED-GRADIENTS FOR INEQUALITY CONSTRAINTS
229 21.3 PENALTY FUNCTIONS FOR INEQUALITY CONSTRAINTS 231 21.4 AL-SUMT
FOR INEQUALITY CONSTRAINTS 233 21.5 SQP FOR INEQUALITY CONSTRAINTS 234
21.6 RESULTS WITH P-SUMT, AL-SUMT AND AL-SQP 235 22. BARRIER FUNCTION
METHODS 239 22.1 PROBLEMS WITH INEQUALITY CONSTRAINTS ONLY 239 22.2
BARRIER FUNCTIONS 241 22.3 RESULTS WITH B-SUMT 244 23. INTERIOR POINT
METHODS 249 23.1 FORMING THE TRANSFORMED PROBLEM B-NLP 249 23.2
APPROXIMATE SOLUTIONS OF PROBLEM B-NLP 250 23.3 AN INTERIOR POINT
ALGORITHM 254 23.4 RESULTS WITH IPM 256 24. A SUMMARY OF CONSTRAINED
METHOD^ 259 25. THE OPTIMA SOFTWARE 261 25.1 ACCESSING OPTIMA 261 25.2
RUNNING OPTIMA 262 CONTENTS IX 25.3 MODIFYING AND CREATING TEST PROBLEMS
262 25.4 MODIFYING OPTIMIZATION METHODS 271 REFERENCES 273 INDEX 27 7 |
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| id | DE-604.BV023476191 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:36:14Z |
| indexdate | 2024-07-09T21:19:38Z |
| institution | BVB |
| isbn | 9780387787220 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016658420 |
| oclc_num | 254885767 |
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| owner | DE-703 DE-29T |
| owner_facet | DE-703 DE-29T |
| physical | XVI, 280 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Springer optimization and its applications |
| series2 | Springer optimization and its applications |
| spelling | Bartholomew-Biggs, Michael C. Verfasser (DE-588)137821816 aut Nonlinear optimization with engineering applications Michael Bartholomew-Biggs 1. ed. Berlin Springer 2008 XVI, 280 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer optimization and its applications 19 Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s Technische Mathematik (DE-588)4827059-3 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-78723-7 Springer optimization and its applications 19 (DE-604)BV021746093 19 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016658420&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bartholomew-Biggs, Michael C. Nonlinear optimization with engineering applications Springer optimization and its applications Nichtlineare Optimierung (DE-588)4128192-5 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| subject_GND | (DE-588)4128192-5 (DE-588)4827059-3 |
| title | Nonlinear optimization with engineering applications |
| title_auth | Nonlinear optimization with engineering applications |
| title_exact_search | Nonlinear optimization with engineering applications |
| title_exact_search_txtP | Nonlinear optimization with engineering applications |
| title_full | Nonlinear optimization with engineering applications Michael Bartholomew-Biggs |
| title_fullStr | Nonlinear optimization with engineering applications Michael Bartholomew-Biggs |
| title_full_unstemmed | Nonlinear optimization with engineering applications Michael Bartholomew-Biggs |
| title_short | Nonlinear optimization with engineering applications |
| title_sort | nonlinear optimization with engineering applications |
| topic | Nichtlineare Optimierung (DE-588)4128192-5 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| topic_facet | Nichtlineare Optimierung Technische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016658420&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021746093 |
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