Global optimization in action: continuous and Lipschitz optimization ; algorithms, implementations and applications
In sciences, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local s...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | Nonconvex optimization and its applications
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | In sciences, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions: hence, it is natural to search for the globally best solution(s) The present volume provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible their straightforward generalizations and extensions, with a view towards efficient computer-based implementations. A considerable part of the book is devoted to various applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained, and is based on its author's research, in cooperation (on applications) with a number of colleagues. Audience : The prospective circle of readers includes professors, students, researchers and other professionals from the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and environmental sciences |
| Beschreibung: | XXVII, 478 S. graph. Darst. |
| ISBN: | 0792337573 |
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| 490 | 1 | |a Nonconvex optimization and its applications |v 6 | |
| 520 | 3 | |a In sciences, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions: hence, it is natural to search for the globally best solution(s) | |
| 520 | |a The present volume provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible their straightforward generalizations and extensions, with a view towards efficient computer-based implementations. A considerable part of the book is devoted to various applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained, and is based on its author's research, in cooperation (on applications) with a number of colleagues. Audience : The prospective circle of readers includes professors, students, researchers and other professionals from the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and environmental sciences | ||
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Datensatz im Suchindex
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| adam_text | GLOBAL OPTIMIZATION IN ACTION CONTINUOUS AND LIPSCHITZ OPTIMIZATION:
ALGORITHMS, IMPLEMENTATIONS AND APPLICATIONS BY JANOS D. PINTER PINTER
CONSULTING SERVICES, DALHOUSIE UNIVERSITY KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS LIST OF FIGURES XIII LIST OF TABLES
XVII PREFACE XIX ACKNOWLEDGEMENTS XXV PART ONE 1 GLOBAL OPTIMIZATION: A
BRIEF REVIEW 1.1 GENERAL PROBLEM STATEMENT AND SPECIAL MODEL FORMS 3
1.1.1 INTRODUCTION 3 1.1.2 CONCAVE MINIMIZATION 6 1.1.3 DIFFERENTIAL
CONVEX (D.C.) PROGRAMMING 10 1.1.4 LIPSCHITZ GLOBAL OPTIMIZATION 14 1.2
SOLUTION APPROACHES 21 1.2.1 GLOBAL VERSUS LOCAL OPTIMIZATION 22 1.2.2
GLOBALIZED LOCAL OPTIMIZATION STRATEGIES, 24 COMBINED WITH GRID SEARCH
OR RANDOM SEARCH 1.2.3 SEQUENTIAL IMPROVEMENT OF LOCAL MINIMA 27 1.2.4
ENUMERATION OF ALL MINIMA 29 1.2.5 RELAXATION (SUCCESSIVE OUTER
APPROXIMATION) STRATEGIES 31 1.2.6 BRANCH-AND-BOUND STRATEGIES 33 1.2.7
CONCLUDING REMARKS 37 VLLL PART TWO 39 PARTITION STRATEGIES IN GLOBAL
OPTIMIZATION: THE CONTINUOUS AND THE LIPSCHITZIAN CASE 2.1 AN
INTRODUCTION TO PARTITION ALGORITHMS 41 2.1.1 PROBLEM STATEMENT AND
BASIC ASSUMPTIONS 41 2.1.2 PARTITION ALGORITHMS: A GENERAL SCHEME 46
2.1.3 UNIFORM GRID SEARCH 48 2.1.4 PIYAVSKII S ALGORITHM 51 2.1.5
KUSHNER S ALGORITHM 56 2.2 CONVERGENCE PROPERTIES OF ADAPTIVE PARTITION
ALGORITHMS 59 2.2.1 REGULAR PARTITION STRATEGIES 59 2.2.2 SUFFICIENT AND
NECESSARY CONVERGENCE CONDITIONS 64 2.3 PARTITION ALGORITHMS ON
INTERVALS 75 2.3.1 CONVERGENCE OF UNIVARIATE GLOBAL OPTIMIZATION
ALGORITHMS 75 2.3.2 AN EFFICIENCY ESTIMATE 85 2.4 PARTITION ALGORITHMS
ON MULTIDIMENSIONAL INTERVALS 91 2.4.1 INTRODUCTION 91 2.4.2 CONVERGENCE
OF MULTIVARIATE RECTANGULAR PARTITION METHODS 97 2.4.3 AN EFFICIENCY
ESTIMATE 100 2.4.4 DECOMPOSABLE PARTITION OPERATORS 104 2.5 SIMPLEX
PARTITION STRATEGIES 111 2.5.1 INTRODUCTION 111 2.5.2 CONVERGENCE OF
SIMPLICIAL ALGORITHMS 115 2.6 PARTITION METHODS ON GENERAL CONVEX AND
STAR SETS 119 2.6.1 INTRODUCTION 119 2.6.2 LIPSCHITZIAN EXTENSION OF THE
OBJECTIVE FUNCTION 120 2.6.3 LINEARLY CONSTRAINED FEASIBLE SETS 125
2.6.4 NONLINEARLY CONSTRAINED CONVEX SETS 127 2.6.5 GENERAL STAR-SHAPED
SETS 129 2.7 PARTITION STRATEGIES IN GENERAL LIPSCHITZ OPTIMIZATION 131
2.7.1 INTRODUCTION 131 2.7.2 A BRANCH-AND-BOUND ALGORITHM SCHEME FOR 132
LIPSCHITZIAN OPTIMIZATION 2.7.3 CONVERGENCE 139 IX PART THREE 145
IMPLEMENTATION ASPECTS, ALGORITHM MODIFICATIONS AND STOCHASTIC
EXTENSIONS 3.1 DIAGONALLY EXTENDED UNIVARIATE ALGORITHMS FOR 147
MULTIDIMENSIONAL GLOBAL OPTIMIZATION 3.1.1 INTRODUCTION 147 3.1.2
DIAGONALLY EXTENDED UNIVARIATE ALGORITHMS 148 3.1.3 EXAMPLES 151 3.2
ESTIMATION OF LIPSCHITZIAN PROBLEM CHARACTERISTICS IN 155 GLOBAL
OPTIMIZATION 3.2.1 INTRODUCTION 155 3.2.2 SUBSET-SPECIFIC ESTIMATES OF
LIPSCHITZIAN CHARACTERISTICS 157 3.2.3 BOUNDING PROCEDURES ON THE BASIS
OF SAMPLE POINTS 158 3.2.4 LIPSCHITZ-CONSTANT ESTIMATION, USING RESULTS
FROM 160 EXTREME ORDER STATISTICS 3.2.5 NUMERICAL COMMENTS AND
CONCLUSIONS 165 3.3 GENERAL LIPSCHITZ OPTIMIZATION APPLYING PENALTY
MULTIPLIERS 169 3.3.1 INTRODUCTION 169 3.3.2 SOLUTION APPROACH 170 3.4
AN IMPLEMENTATION OF A LIPSCHITZIAN GLOBAL 173 OPTIMIZATION PROCEDURE
3.4.1 THE LGO PROGRAM SYSTEM 173 3.4.2 CURRENT SYSTEM REQUIREMENTS AND
PROBLEM SIZE 177 LIMITATIONS 3.4.3 USING LGO IN AN INTERACTIVE
ENVIRONMENT 179 3.4.4 ILLUSTRATIVE TEST RESULTS 183 3.5 DECISION MAKING
UNDER UNCERTAINTY: STOCHASTIC MODEL FORMS 191 3.5.1 INTRODUCTION 191
3.5.2 MODEL VARIANTS AND SOLUTION APPROACHES 193 3.5.3 CONCLUSIONS 202
3.6 ADAPTIVE STOCHASTIC OPTIMIZATION PROCEDURES 205 3.6.1 INTRODUCTION
205 3.6.2 CONVERGENCE OF RANDOM SEARCH BASED STOCHASTIC 207 OPTIMIZATION
METHODS 3.6.3 CONVERGENCE OF STOCHASTICALLY COMBINED 216 OPTIMIZATION
PROCEDURES 3.7 ESTIMATION OF NOISE-PERTURBED FUNCTION VALUES 227 3.7.1
INTRODUCTION 227 3.7.2 ESTIMATION OF NOISY FUNCTION VALUES 228 3.7.3
ESTIMATION OF PROBABILITIES 232 PART FOUR 237 APPLICATIONS INTRODUCTORY
NOTES 239 4.1 NONLINEAR APPROXIMATION: SYSTEMS OF EQUATIONS 241 AND
INEQUALITIES 4.1.1 INTRODUCTION 241 4.1.2 SYSTEMS OF NONLINEAR EQUATIONS
243 4.1.3 NONLINEAR EQUATIONS AND EQUIVALENT GLOBAL 244 OPTIMIZATION
PROBLEMS 4.1.4 TEST RESULTS ON RANDOMLY GENERATED SYSTEMS 249 OF
EQUATIONS 4.1.5 LIPSCHITZIAN EQUATIONS AND INEQUALITIES 258 4.1.6
CONCLUDING REMARKS 259 4.2 DATA CLASSIFICATION (CLUSTERING) AND RELATED
PROBLEMS 261 4.2.1 INTRODUCTION 261 4.2.2 DATA CLASSIFICATION: PROBLEM
STATEMENT AND EXAMPLES 263 4.2.3 CLASSIFICATION PROCEDURES BASED ON
CLUSTER SEED POINTS 266 4.2.4 SELECTING SPM APPLYING GLOBAL OPTIMIZATION
269 4.2.5 NUMERICAL EXAMPLES 270 4.2.6 CONCLUDING REMARKS 274 4.3
AGGREGATION OF NEGOTIATED EXPERT OPINIONS 277 4.3.1 INTRODUCTION 277
4.3.2 A GENERAL MODEL FOR COMBINING NEGOTIATED 279 EXPERT OPINIONS 4.3.3
MODEL SPECIFICATIONS 281 4.3.4 SOLUTION APPROACH BASED ON LIPSCHITZ 285
GLOBAL OPTIMIZATION 4.3.5 NUMERICAL EXAMPLES 287 4.3.6 CONCLUSIONS 293
XI 4.4 PRODUCT (MIXTURE) DESIGN 295 4.4.1 INTRODUCTION 295 4.4.2
SOLUTION APPROACH 298 4.4.3 CALCULATION OF LOWER BOUNDS 299 4.4.4
NUMERICAL EXAMPLES AND REMARKS 300 4.5 GLOBALLY OPTIMIZED CALIBRATION OF
COMPLEX SYSTEM MODELS 303 4.5.1 INTRODUCTION 303 4.5.2 MODEL
CALIBRATION: A GENERAL PROBLEM STATEMENT 306 4.5.3 BASIC UNDERLYING
ASSUMPTIONS 308 4.5.4 DISCRETIZATION 309 4.5.5 STATISTICAL UNCERTAINTIES
AND ROBUST CALIBRATION 309 4.5.6 MULTIPLE CALIBRATION OBJECTIVES 312
4.5.7 MULTIEXTREMALITY 314 4.6 CALIBRATION MODEL VERSIONS, ILLUSTRATED
BY EXAMPLES 317 4.6.1 INTRODUCTION 317 4.6.2 AVERAGE Z P -DISTANCE AND
VARIANTS 318 4.6.3 DISCREPANCY MEASURES FOR CALIBRATING SOFT SYSTEMS
321 4.6.4 A SEDIMENT-WATER INTERACTION MODEL FOR SHALLOW LAKES 328 4.6.5
A CHEMICAL FATE MODEL 331 4.6.6 A RIVER FLOW MODEL 334 4.7 DYNAMIC
MODELLING OF PHOSPHORUS RELEASE FROM SEDIMENTS 341 4.7.1 INTRODUCTION
341 4.7.2 NUMERICAL RESULTS AND DISCUSSION 343 4.7.3 CONCLUSIONS ; 352
4.8 AQUIFER MODEL CALIBRATION 353 4.8.1 INTRODUCTION 353 4.8.2 STUDY
AREA 355 4.8.3 AQUIFER MODEL 356 4.8.4 SELECTION OF OPTIMIZED PARAMETERS
357 4.8.5 SOLUTION APPROACH 358 4.8.6 NUMERICAL RESULTS AND DISCUSSION
358 4.8.7 CONCLUSIONS 360 4.9 INDUSTRIAL WASTEWATER MANAGEMENT 361 4.9.1
INTRODUCTION 361 4.9.2 ENVIRONMENT-ECONOMY INTEGRATION IN MODELLING 362
4.9.3 WASTEWATER TREATMENT ENGINEERING SYSTEM MODEL 363 XLL 4.9.4
ANALYTICAL OPTIMIZATION MODEL 370 4.9.5 SOLUTION APPROACHES 372 4.9.6
IMPLEMENTATION ASPECTS 376 4.9.7 ILLUSTRATIVE NUMERICAL RESULTS AND
DISCUSSION 377 4.10 MULTIPLE SOURCE RIVER POLLUTION MANAGEMENT 383
4.10.1 INTRODUCTION 383 4.10.2 MODELLING 384 4.10.3 SOLUTION METHOD 388
4.10.4 ILLUSTRATIVE RESULTS AND DISCUSSION 389 4.11 LAKE EUTROPHICATION
MANAGEMENT 395 4.11.1 INTRODUCTION 395 4.11.2 LAKE EUTROPHICATION:
MANAGEMENT ALTERNATIVES 396 4.11.3 DECOMPOSITION AND AGGREGATION 397
4.11.4 A STOCHASTIC MODELLING FRAMEWORK 400 4.11.5 SOLUTION METHOD 403
4.11.6 SUMMARY OF RESULTS AND CONCLUSIONS 403 4.12 RISK MANAGEMENT OF
ACCIDENTAL WATER POLLUTION 407 4.12.1 INTRODUCTION 407 4.12.2 RISK
ASSESSMENT AND MANAGEMENT: PRINCIPLES, 408 MODELS, SOLUTION METHODS
4.12.3 AN ILLUSTRATIVE CASE STUDY 411 4.12.4 QUANTITATIVE ANALYSIS 413
4.12.5 NUMERICAL EXAMPLE AND DISCUSSION 420 AFTERWORD 423 SOME FURTHER
RESEARCH PERSPECTIVES 425 REFERENCES 431 INDEX 473
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| spelling | Pintér, János D. Verfasser (DE-588)1192712978 aut Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications by János D. Pintér Dordrecht [u.a.] Kluwer 1996 XXVII, 478 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 6 In sciences, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions: hence, it is natural to search for the globally best solution(s) The present volume provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible their straightforward generalizations and extensions, with a view towards efficient computer-based implementations. A considerable part of the book is devoted to various applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained, and is based on its author's research, in cooperation (on applications) with a number of colleagues. Audience : The prospective circle of readers includes professors, students, researchers and other professionals from the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and environmental sciences Niet-lineaire programmering gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Nichtkonvexe Optimierung (DE-588)4309215-9 gnd rswk-swf Nichtkonvexe Optimierung (DE-588)4309215-9 s DE-604 Nonconvex optimization and its applications 6 (DE-604)BV010085908 6 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007115256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pintér, János D. Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications Nonconvex optimization and its applications Niet-lineaire programmering gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| subject_GND | (DE-588)4309215-9 |
| title | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications |
| title_auth | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications |
| title_exact_search | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications |
| title_full | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications by János D. Pintér |
| title_fullStr | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications by János D. Pintér |
| title_full_unstemmed | Global optimization in action continuous and Lipschitz optimization ; algorithms, implementations and applications by János D. Pintér |
| title_short | Global optimization in action |
| title_sort | global optimization in action continuous and lipschitz optimization algorithms implementations and applications |
| title_sub | continuous and Lipschitz optimization ; algorithms, implementations and applications |
| topic | Niet-lineaire programmering gtt Optimaliseren gtt Mathematical optimization Nonlinear programming Nichtkonvexe Optimierung (DE-588)4309215-9 gnd |
| topic_facet | Niet-lineaire programmering Optimaliseren Mathematical optimization Nonlinear programming Nichtkonvexe Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007115256&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT pinterjanosd globaloptimizationinactioncontinuousandlipschitzoptimizationalgorithmsimplementationsandapplications |