Convexification and global optimization in continuous and mixed-integer nonlinear programming: theory, algorithms, software, and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Kluwer Academic Publishers
2002
|
| Schriftenreihe: | Nonconvex optimization and its applications
65 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index |
| Beschreibung: | xxv, 475 Seiten Illustrationen, Diagramme |
| ISBN: | 9781402010316 1402010311 |
Internformat
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| 245 | 1 | 0 | |a Convexification and global optimization in continuous and mixed-integer nonlinear programming |b theory, algorithms, software, and applications |c by Mohit Tawarmalani and Nikolaos V. Sahinidis |
| 264 | 1 | |a Dordrecht |b Kluwer Academic Publishers |c 2002 | |
| 300 | |a xxv, 475 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Nonconvex optimization and its applications |v 65 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Nonlinear programming | |
| 650 | 0 | 7 | |a Globale Optimierung |0 (DE-588)4140067-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gemischt-ganzzahlige Optimierung |0 (DE-588)4156566-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Globale Optimierung |0 (DE-588)4140067-7 |D s |
| 689 | 0 | 1 | |a Gemischt-ganzzahlige Optimierung |0 (DE-588)4156566-6 |D s |
| 689 | 0 | 2 | |a Nichtlineare Optimierung |0 (DE-588)4128192-5 |D s |
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Datensatz im Suchindex
| _version_ | 1804129663651414016 |
|---|---|
| adam_text | Contents
Preface
Acknowledgments
List of Figures
List of Tables
1
1.1
1.2
1.3
1.3.1
1.3.2
1.3.3
1.3.4
1.3.5
1.4
2
2.1
2.2
2.3
2.4
2.4.1
2.4.2
2.4.3
2.4.4
2.4.5
2.4.6
2.4.7
2.5
2.5.1
2.5.2
2.5.3
2.5.4
3
3.1
3.2
3.3
3.4
3.5
3.6
3.6.1
3.6.2
3.6.3
3.7
3.8
3.9
3.10
3.11
3.11.1
3.11.2
3.11.3
4
4.1
4.1.1
4.2
5
5.1
5.1.1
5.1.2
5.2
5.3
5.4
5.5
5.6
5.7
5.7.1
5.7.2
5.7.3
5.8
5.9
6
6.1
6.2
6.2.1
6.2.2
6.3
6.3.1
6.3.2
6.3.3
6.3.4
6.3.5
6.3.6
6.3.7
6.3.8
6.3.9
6.3.10
7
7.1
7.2
7.3
7.4
7.4.1
7.4.2
7.4.3
7.5
7.6
7.6.1
7.6.2
7.6.3
7.6.4
7.7
7.8
8
8.1
8.2
8.3
8.4
8.4.1
8.4.2
8.5
8.6
9
9.1
9.2
9.2.1
9.2.2
9.3
9.3.1
9.3.2
9.4
9.4.1
9.4.2
10
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.7.1
10.7.2
11
11.1
11.2
11.2.1
МІР,
11.2.2
Factorable Nonlinear Programming Solver
11.3
11.4
11.4.1
11.4.2
11.5
11.6
11.6.1
11.6.2
11.7
11.8
11.8.1
11.8.2
11.8.3
tions
11.8.4
11.8.5
11.8.6
11.8.7
11.8.8
11.8.9
11.9
11.9.1
11.9.2
11.9.3
11.9.4
11.9.5
11.9.6
11.10
11.11
xii CONTENTS
11.12
11.12.1
11.12.2
Problems
11.12.3
11.12.4
tions
A GAMS Models for Pooling Problems
A.I Problems Adhya
A.2 Problems Bental
A.3 Problems Foulds
A.4 Problems Haverly
A.5 Problem RT
Bibliography
Index
Author Index
CONVEXIFICATION AND GLOBAL OPTIMIZATION IN CONTINUOUS AND MIXED-INTEGER
NONLINEAR PROGRAMMING THEORY, ALGORITHMS, SOFTWARE, AND APPLICATIONS BY
MOHIT TAWARMALANI PURDUE UNIVERSITY, WEST LAFAYETTE, IN, U.S.A. AND
NIKOLAOS V. SAHINIDIS UNIVERSITY OF ILLINOIS, URBANA, IL, U.S.A. §3!
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS PREFACE
XIII ACKNOWLEDGMENTS XVII LIST OF FIGURES XIX LIST OF TABLES XXIII 1
INTRODUCTION 1 1.1 THE MIXED-INTEGER NONLINEAR PROGRAM 5 1.2
BRANCH-AND-BOUND 6 1.3 ILLUSTRATIVE EXAMPLE 8 1.3.1 A SEPARABLE
RELAXATION 9 1.3.2 TIGHTER RELAXATION 12 1.3.3 OPTIMALITY-BASED RANGE
REDUCTION 12 1.3.4 DRAWING INFERENCES FROM CONSTRAINTS 16 1.3.5
BRANCHING ON THE INCUMBENT 17 1.4 OUTLINE OF THIS BOOK 18 2 CONVEX
EXTENSIONS 25 2.1 INTRODUCTION 26 2.2 CONVEX EXTENSIONS OF L.S.C.
FUNCTIONS 29 2.3 MULTILINEAR FUNCTIONS 40 2.4 ANALYSIS OF CONVEX
UNDERESTIMATORS OF X/Y 43 2.4.1 CONVEX ENVELOPE OF X/Y 44 2.4.2
CLOSED-FORM EXPRESSION OF CONVEX ENVELOPE 45 2.4.3 THEORETICAL
COMPARISON OF UNDERESTIMATORS 47 2.4.4 NUMERICAL EXAMPLE 52 VN VIII
CONTENTS 2.4.5 CONCAVE ENVELOPE OF X/Y 56 2.4.6 RELAXING THE POSITIVITY
REQUIREMENT 57 2.4.7 SEMIDEFINITE RELAXATION OF X/Y 60 2.5
GENERALIZATIONS AND APPLICATIONS 62 2.5.1 ENVELOPES OF (AX + BY)/(EX +
DY) 64 2.5.2 CONVEX ENVELOPE OF F(X)Y 2 65 2.5.3 CONVEX ENVELOPE OF
F(X)/Y 69 2.5.4 SUMMATION OF FUNCTIONS 69 3 PRODUCT DISAGGREGATION 71
3.1 INTRODUCTION 72 3.2 PRELIMINARIES 75 3.3 REFORMULATIONS OF A
RATIONAL FUNCTION 77 3.4 TIGHTNESS OF THE REFORMULATION SCHEME 81 3.5
SPECIAL INSTANCES OF THE REFORMULATION 91 3.6 EXAMPLES OF THE
REFORMULATION SCHEME 93 3.6.1 EXAMPLE 1: HOCK & SCHITTKOWSKI (1981) 94
3.6.2 EXAMPLE 2: NUCLEAR REACTOR RELOAD PATTERN DESIGN . 95 3.6.3
EXAMPLE 3: CATALYST MIXING FOR PACKED BED REACTOR 97 3.7 REFORMULATIONS
OF HYPERBOLIC PROGRAMS 100 3.8 UPPER BOUNDING OF 0*1 HYPERBOLIC PROGRAMS
105 3.9 A BRANCH-AND-BOUND ALGORITHM 108 3.10 CARDINALITY CONSTRAINED
HYPERBOLIC PROGRAMS 110 3.11 COMPUTATIONAL RESULTS FOR CCH PROGRAMS ILL
3.11.1 COMPARISON OF BOUNDS 112 3.11.2 PERFORMANCE OF THE PROPOSED
ALGORITHM 112 3.11.3 P-CHOICE FACILITY LOCATION 115 4 RELAXATIONS OF
FACTORABLE PROGRAMS 125 4.1 NONLINEAR RELAXATION CONSTRUCTION 125 4.1.1
CONCAVOCONVEX FUNCTIONS 130 4.2 POLYHEDRAL OUTER-APPROXIMATION 132 5
DOMAIN REDUCTION 147 5.1 PRELIMINARIES 147 5.1.1 LEGENDRE-FENCHEL
TRANSFORM 148 5.1.2 LAGRANGIAN RELAXATION 152 5.2 AN ITERATIVE ALGORITHM
FOR DOMAIN REDUCTION 153 CONTENTS IX 5.3 THEORETICAL FRAMEWORK: ABSTRACT
MINIMIZATION 154 5.4 APPLICATION TO TRADITIONAL MODELS 160 5.5 GEOMETRIC
INTUITION 163 5.6 DOMAIN REDUCTION PROBLEM: MOTIVATION 163 5.7 RELATION
TO EARLIER WORKS 164 5.7.1 BOUNDS VIA MONOTONE COMPLEMENTARITY . . . . .
. . 177 5.7.2 TIGHTENING USING REDUCED COSTS 178 5.7.3 LINEARITY-BASED
TIGHTENING 179 5.8 PROBING 181 5.9 LEARNING REDUCTION PROCEDURE 183 6
NODE PARTITIONING 189 6.1 INTRODUCTION 189 6.2 PARTITIONING FACTORABLE
PROGRAMS 190 6.2.1 BRANCHING VARIABLE SELECTION 190 6.2.2 BRANCHING
POINT SELECTION ... 194 6.3 FINITENESS ISSUES 196 6.3.1 STOCHASTIC
INTEGER PROGRAMS 197 6.3.2 THE QUESTION OF FINITENESS 198 6.3.3 KEY TO
FINITENESS 199 6.3.4 LOWER BOUNDING PROBLEM 200 . 6.3.5 UPPER BOUNDING
202 6.3.6 BRANCHING SCHEME 203 6.3.7 FINITENESS PROOF 205 6.3.8
ENHANCEMENTS 205 6.3.9 EXTENSION TO MIXED-INTEGER RECOURSE 207 6.3.10
COMPUTATIONAL RESULTS FOR STOCHASTIC PROGRAMS . . . 207 7 IMPLEMENTATION
213 7.1 DESIGN PHILOSOPHY 213 7.2 PROGRAMMING LANGUAGES AND PORTABILITY
215 7.3 SUPPORTED OPTIMIZATION SOLVERS V 216 7.4 DATA STORAGE AND
ASSOCIATED ALGORITHMS 216 7.4.1 MANAGEMENT OF WORK-ARRAY 216 7.4.2 LIST
OF OPEN NODES 217 7.4.3 MODULE STORAGE: FACTORABLE PROGRAMMING 218 7.5
EVALUATING DERIVATIVES 219 7.6 ALGORITHMIC ENHANCEMENTS 221 X CONTENTS
7.6.1 MULTIPLE SOLUTIONS 221 7.6.2 LOCAL UPPER BOUNDS 222 7.6.3
POSTPONEMENT 222 7.6.4 FINITE BRANCHING SCHEMES 223 7.7 DEBUGGING
FACILITIES 224 7.8 BARON INTERFACE 224 8 REFRIGERANT DESIGN PROBLEM 229
8.1 INTRODUCTION 229 8.2 PROBLEM STATEMENT 230 8.3 PREVIOUS WORK 231 8.4
OPTIMIZATION FORMULATION 232 8.4.1 MODELING PHYSICAL PROPERTIES 235
8.4.2 MODELING STRUCTURAL CONSTRAINTS 239 8.5 MULTIPLE SOLUTIONS 249 8.6
COMPUTATIONAL RESULTS 249 9 THE POOLING PROBLEM 253 9.1 INTRODUCTION 254
9.2 THE P- AND Q-FORMULATIONS 256 9.2.1 THE P-FORMULATION 256 9.2.2 THE
Q-FORMULATION 261 9.3 THE PQ-FORMULATION 264 9.3.1 PROPERTIES OF THE
PQ-FORMULATION 266 9.3.2 LAGRANGIAN RELAXATIONS 273 9.4 GLOBAL
OPTIMIZATION OF THE POOLING PROBLEM 276 9.4.1 BRANCHING STRATEGY 278
9.4.2 COMPUTATIONAL EXPERIENCE 279 10 MISCELLANEOUS PROBLEMS 285 10.1
SEPARABLE CONCAVE QUADRATIC PROGRAMS 285 10.2 INDEFINITE QUADRATIC
PROGRAMS -. 289 10.3 LINEAR MULTIPLICATIVE PROGRAMS 293 10.4 GENERALIZED
LINEAR MULTIPLICATIVE PROGRAMS 297 10.5 UNIVARIATE POLYNOMIAL PROGRAMS
298 10.6 MISCELLANEOUS BENCHMARK PROBLEMS 298 10.7 SELECTED
MIXED-INTEGER NONLINEAR PROGRAMS 305 10.7.1 DESIGN OF JUST-IN-TIME
FLOWSHOPS 305 CONTENTS XI 10.7.2 THE GUPTA-RAVINDRAN BENCHMARKS 311 11
GAMS/BARON: A TUTORIAL 313 11.1 INTRODUCTION 314 11.2 TYPES OF PROBLEMS
GAMS/BARON CAN SOLVE 315 11.2.1 FACTORABLE NONLINEAR PROGRAMMING: MIP,
NLP, AND MINLP 315 11.2.2 SPECIAL CASES OF BARON S FACTORABLE NONLINEAR
PROGRAMMING SOLVER 316 11.3 SOFTWARE AND HARDWARE REQUIREMENTS 320 11.4
MODEL REQUIREMENTS 320 11.4.1 VARIABLE AND EXPRESSION BOUNDS 320 11.4.2
ALLOWABLE NONLINEAR FUNCTIONS 321 11.5 HOW TO RUN GAMS/BARON 321 11.6
SYSTEM OUTPUT 322 11.6.1 SYSTEM LOG 322 11.6.2 TERMINATION MESSAGES,
MODEL AND SOLVER STATUS . . . 324 11.7 ALGORITHMIC AND SYSTEM OPTIONS
325 11.8 APPLICATION TO MULTIPLICATIVE PROGRAMS 325 11.8.1 LMPS OF TYPE
1 326 11.8.2 CONTROLLING LOCAL SEARCH REQUIREMENTS 329 11.8.3 REDUCING
MEMORY REQUIREMENTS VIA BRANCHING OP- TIONS 331 11.8.4 CONTROLLING
MEMORY REQUIREMENTS VIA PROBING . . . 333 11.8.5 EFFECTS OF
REFORMULATION 334 11.8.6 LMPS OF TYPE 2 335 11.8.7 CONTROLLING TIME
SPENT ON PREPROCESSING LPS .... 339 11.8.8 LMPS OF TYPE 3 342 11.8.9
COMPARISON WITH LOCAL SEARCH 347 11.9 APPLICATION TO POOLING PROBLEMS
356 11.9.1 CONTROLLING TIME SPENT IN PREPROCESSING 364 11.9.2 REDUCING
MEMORY REQUIREMENTS 368 11.9.3 CONTROLLING THE SIZE OF THE SEARCH TREE
368 11.9.4 CONTROLLING LOCAL SEARCH TIME DURING NAVIGATION . . 371
11.9.5 REDUCED BRANCHING SPACE 371 11.9.6 POOLING PROBLEM COMPUTATIONS
372 11.10 PROBLEMS FROM GLOBALLIB AND MINLPLIB 376 11.11 LOCAL LANDSCAPE
ANALYZER 380 XII CONTENTS 11.12 FINDING THE K BEST OR ALL FEASIBLE
SOLUTIONS 383 11.12.1 MOTIVATION AND ALTERNATIVE APPROACHES 383 11.12.2
FINDING ALL SOLUTIONS TO COMBINATORIAL OPTIMIZATION PROBLEMS 385 11.12.3
REFRIGERANT DESIGN PROBLEM 391 11.12.4 FINDING ALL SOLUTIONS TO SYSTEMS
OF NONLINEAR EQUA- TIONS 394 A GAMS MODELS FOR POOLING PROBLEMS 403 A.I
PROBLEMS ADHYA 1, 2, 3, AND 4 403 A.2 PROBLEMS BENTAL 4 AND 5 411 A.3
PROBLEMS FOULDS 2, 3, 4, AND 5 416 A.4 PROBLEMS HAVERLY 1, 2, AND 3 428
A.5 PROBLEM RT 2 431 BIBLIOGRAPHY 435 INDEX 463 AUTHOR INDEX 469
|
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| ctrlnum | (OCoLC)51047079 (DE-599)BVBBV014936212 |
| dewey-full | 519.7/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/6 |
| dewey-search | 519.7/6 |
| dewey-sort | 3519.7 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014936212 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:43Z |
| institution | BVB |
| isbn | 9781402010316 1402010311 |
| language | English |
| lccn | 2002040741 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010079915 |
| oclc_num | 51047079 |
| open_access_boolean | |
| owner | DE-384 DE-11 DE-29T DE-634 |
| owner_facet | DE-384 DE-11 DE-29T DE-634 |
| physical | xxv, 475 Seiten Illustrationen, Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Academic Publishers |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Tawarmalani, Mohit Verfasser aut Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications by Mohit Tawarmalani and Nikolaos V. Sahinidis Dordrecht Kluwer Academic Publishers 2002 xxv, 475 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 65 Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 s Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Sahinidis, Nikolaos V. Sonstige oth Nonconvex optimization and its applications 65 (DE-604)BV010085908 65 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079915&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079915&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tawarmalani, Mohit Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications Nonconvex optimization and its applications Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4128192-5 (DE-588)4156566-6 |
| title | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications |
| title_auth | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications |
| title_exact_search | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications |
| title_full | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications by Mohit Tawarmalani and Nikolaos V. Sahinidis |
| title_fullStr | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications by Mohit Tawarmalani and Nikolaos V. Sahinidis |
| title_full_unstemmed | Convexification and global optimization in continuous and mixed-integer nonlinear programming theory, algorithms, software, and applications by Mohit Tawarmalani and Nikolaos V. Sahinidis |
| title_short | Convexification and global optimization in continuous and mixed-integer nonlinear programming |
| title_sort | convexification and global optimization in continuous and mixed integer nonlinear programming theory algorithms software and applications |
| title_sub | theory, algorithms, software, and applications |
| topic | Mathematical optimization Nonlinear programming Globale Optimierung (DE-588)4140067-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd Gemischt-ganzzahlige Optimierung (DE-588)4156566-6 gnd |
| topic_facet | Mathematical optimization Nonlinear programming Globale Optimierung Nichtlineare Optimierung Gemischt-ganzzahlige Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079915&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010079915&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT tawarmalanimohit convexificationandglobaloptimizationincontinuousandmixedintegernonlinearprogrammingtheoryalgorithmssoftwareandapplications AT sahinidisnikolaosv convexificationandglobaloptimizationincontinuousandmixedintegernonlinearprogrammingtheoryalgorithmssoftwareandapplications |
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