Deterministic global optimization: theory, methods and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
2000
|
| Series: | Nonconvex optimization and its applications
37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 739 S. graph. Darst. |
| ISBN: | 0792360141 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | IMAGE 1
DETERMINISTIC GLOBAL
OPTIMIZATION THEORY^ METHODS AND APPLICATIONS
BY
CHRISTODOULOS A. FLOUDAS
DEPARTMENT OF CHEMICAL ENGINEERING, PRINCETON UNIVERSITY, PRINCETON, NEW
JERSEY, U.S.A.
W
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE X I II
1. INTRODUCTION 1
1.1 MOTIVATION 1
1.2 STRUCTURE OF GLOBAL OPTIMIZATION MODELS 3
1.3 ILLUSTRATIVE APPLICATIONS OF GLOBAL OPTIMIZATION 4
1.4 DETERMINISTIC GLOBAL OPTIMIZATION : APPROACHES AND CLASSES OF
PROBLEMS 18
1.5 COMPLEXITY ANALYSIS 19
1.6 RESEARCH AREAS AND IMPORTANT APPLICATIONS 23
1.7 PUBLICATIONS AND CONFERENCES 25
1.8 CHEMICAL ENGINEERING CONTRIBUTIONS 27
1.9 SCOPE OF THE BOOK 32
2. BASIC CONCEPTS OF GLOBAL OPTIMIZATION 33
2.1 CONVEX SETS 33
2.2 CONVEX AND CONCAVE FUNCTIONS 35
2.3 QUASI-CONVEX AND PSEUDO-CONVEX FUNCTIONS 42
2.4 CONVEX ENVELOPES 45
2.5 LOCAL, GLOBAL, E-GLOBAL MINIMA 57
2.6 DIFFERENCE OF CONVEX (D.C.) FUNCTIONS 58
PART I BICONVEX AND BILINEAR PROBLEMS
3. THE GOPPRIMAL-RELAXED DUAL DECOMPOSITION APPROACH : THEORY 67
3.1 PROBLEM STATEMENT 68
3.2 DUALITY THEORY 70
3.3 MATHEMATICAL PROPERTIES 73
3.4 INFEASIBLE PRIMAL PROBLEMS 82
3.5 THE GLOBAL OPTIMIZATION (GOP) ALGORITHM 84
3.6 FINITE E-CONVERGENCE AND E-GLOBAL OPTIMALITY 87
3.7 ILLUSTRATIVE EXAMPLE 90
XM
IMAGE 3
VUEI DETERMINISTIC GLOBAL OPTIMIZATION
3.8 THE GOP FOR QUADRATIC PROBLEMS WITH LINEAR CONSTRAINTS 95
3.9 THE GOP FOR QUADRATICALLY CONSTRAINED PROBLEMS 96
3.10 THE GOP FOR UNIVARIATE POLYNOMIAL PROBLEMS 98
3.11 ADDITIONAL PROPERTIES OF THE LAGRANGE FUNCTION 105
3.12 THE GOP IN A BRANCH AND BOUND FRAMEWORK 114
3.13 REFORMULATION OF THE RELAXED DUAL AS A SINGLE MILP PROBLEM 126
3.14 A LINEAR BRANCHING SCHEME FOR THE GOP ALGORITHM 134
4. THE GOP APPROACH : IMPLEMENTATION AND COMPUTATIONAL STUDIES141
4.1 IMPLEMENTATION OF THE GOP AND GOP/MILP ALGORITHMS 141
4.2 COMPUTATIONAL STUDIES 152
4.3 SUMMARY 168
5. THE GOP APPROACH IN BILEVEL LINEAR AND QUADRATIC PROBLEMS 173
5.1 INTRODUCTION 173
5.2 BILEVEL LINEAR PROGRAMMING PROBLEM 175
5.3 MODIFIED GOP ALGORITHM 181
5.4 BILEVEL LINEAR-QUADRATIC AND BILEVEL QUADRATIC-QUADRATIC PROBLEMS
187
6. THE GOP APPROACH IN PHASE AND CHEMICAL EQUILIBRIUM PROBLEMS 193
6.1 INTRODUCTION AND FORMULATION OF MINIMIZING THE GIBBS FREE ENERGY 193
6.2 APPLICATION OF THE GOP TO NRTL EQUATION 198
6.3 COMPUTATIONAL STUDIES 212
6.4 TANGENT PLANE STABILITY CRITERION 225
6.5 APPLICATION TO THE NRTL EQUATION 229
6.6 ILLUSTRATIVE EXAMPLE FOR THE NRTL : N-BUTYL-ACETATE - WATER 234
7. THE GOP APPROACH : DISTRIBUTED IMPLEMENTATION 243
7.1 CRITICAL COMPONENTS OF THE DISTRIBUTED GOP APPROACH 243
7.2 LARGE SCALE INDEFINITE QUADRATIC PROBLEMS 247
7.3 LARGE SCALE POOLING AND BLENDING PROBLEMS 251
PART II SIGNOMIAL PROBLEMS
8. GENERALIZED GEOMETRIC PROGRAMMING : THEORY 257
8.1 INTRODUCTION 257
8.2 THEORETICAL ANALYSIS 261
8.3 GLOBAL OPTIMIZATION ALGORITHM , 276
8.4 PROOF OF CONVERGENCE TO THE GLOBAL MINIMUM 282
8.5 ILLUSTRATIVE EXAMPLE 283
9. GENERALIZED GEOMETRIC PROGRAMMING : COMPUTATIONAL STUDIES 289
9.1 CHEMICAL ENGINEERING DESIGN EXAMPLES 289
9.2 ROBUST STABILITY ANALYSIS 297
IMAGE 4
CONTENTS IX
PART III TOWARDS GENERAL TWICE DIFFERENTIABLE NLPS
10. FROM BICONVEX TO GENERAL TWICE DIFFERENTIABLE NLPS 309
10.1 THEORETICAL RESULTS : GOP TO A BB 309
10.2 ESTIMATION OF THE PARAMETER A 311
11. THE A BB FOR BOX CONSTRAINED TWICE-DIFFERENTIABLE NLPS : THEORY315
11.1 FORMULATION AND D.C. TRANSFORMATION 315
11.2 CONVEX LOWER BOUNDING FUNCTION 318
11.3 GLOBAL OPTIMIZATION ALGORITHM A BB 323
11.4 STEPS OF THE GLOBAL OPTIMIZATION ALGORITHM A BB 324
11.5 PROOF OF CONVERGENCE TO THE GLOBAL MINIMUM 326
11.6 COMPLEXITY ANALYSIS 329
12. THE A BB FOR CONSTRAINED TWICE -DIFFERENTIABLE NLPS : THEORY 333
12.1 FORMULATION AND PRINCIPLES OF THE A BB GLOBAL OPTIMIZATION
ALGORITHM 334
12.2 UNDERESTIMATION STRATEGIES 334
12.3 OVERALL VALID CONVEX UNDERESTIMATOR 340
12.4 RIGOROUS CALCULATION OF A FOR GENERAL NLPS 342
12.5 ILLUSTRATIVE EXAMPLE 355
12.6 GLOBAL OPTIMIZATION ALGORITHM, A BB 361
12.7 GEOMETRICAL INTERPRETATION OF THE A BB APPROACH 365
13. COMPUTATIONAL STUDIES OF THE A BB APPROACH 377
13.1 ALGORITHMIC ISSUES AND DEVELOPMENT OF THE A BB 377
13.2 IMPLEMENTATION OF THE A BB 382
13.3 COMPUTATIONAL STUDIES OF THE A BB APPROACH 384
14. GLOBAL OPTIMIZATION IN MICROCLUSTERS 403
14.1 INTRODUCTION 403
14.2 PROBLEM DEFINITION 407
14.3 NOVEL D.C. TRANSFORMATION VIA EIGENVALUE ANALYSIS 409
14.4 MATHEMATICAL MODEL 418
14.5 ALGORITHMIC PROCEDURE 423
14.6 SMALL CLUSTER EXAMPLES 425
14.7 A RELAXATION OF THE GLOBAL OPTIMIZATION APPROACH 426
14.8 DISCUSSION ON MAGIC NUMBERS AND INTERATOMIC SPACING 431
14.9 SUMMARY 432
15. THE A BB APPROACH IN MOLECULAR STRUCTURE PREDICTION 435
15.1 INTRODUCTION AND BACKGROUND 435
15.2 PROBLEM DEFINITION 438
15.3 PROBLEM REFORMULATION IN INTERNAL COORDINATES 439
15.4 CONVEX LOWER BOUNDING FUNCTION L OF V 444
15.5 COMPUTATIONAL STUDY : PROPANAL 447
IMAGE 5
DETERMINISTIC GLOBAL OPTIMIZATION
16. THE A BB APPROACH IN PROTEIN FOLDING 451
16.1 INTRODUCTION 451
16.2 MATHEMATICAL MODELING 452
16.3 GLOBAL OPTIMIZATION 459
16.4 COMPUTATIONAL STUDIES : UNSOLVATED OLIGOPEPTIDES 466
16.5 COMPUTATIONAL STUDIES : SOLVATED OLIGOPEPTIDES 471
17. THE A BB APPROACH IN PEPTIDE DOCKING 481
17.1 INTRODUCTION 481
17.2 PEPTIDE DOCKING METHODS 483
17.3 PROBLEM DEFINITION 485
17.4 OUTLINE OF APPROACH 488
17.5 MATHEMATICAL MODELING AND PROBLEM FORMULATION 490
17.6 GLOBAL OPTIMIZATION APPROACH AND ITS INTERFACE 493
17.7 COMPUTATIONAL STUDIES AND DISCUSSION 498
18. THE A BB APPROACH IN BATCH DESIGN UNDER UNCERTAINTY 507
18.1 INTRODUCTION 507
18.2 MULTIPRODUCT DESIGN PROBLEM 509
18.3 LOWER BOUNDING PROBLEM FORMULATIONS 517
18.4 GLOBAL OPTIMIZATION ALGORITHM - MODIFIED A BB 524
18.5 ILLUSTRATIVE EXAMPLE 528
18.6 MIXED-PRODUCT CAMPAIGN FORMULATION 530
18.7 COMPUTATIONAL STUDIES 533
18.8 COMPARISON TO ALTERNATIVE UNDERESTIMATING APPROACHES 538
19. THE A BB APPROACH IN PARAMETER ESTIMATION 543
19.1 INTRODUCTION 543
19.2 MAXIMUM LIKELIHOOD ESTIMATION 545
19.3 GLOBAL OPTIMIZATION FRAMEWORK 548
19.4 GLOBAL OPTIMIZATION ALGORITHM 551
19.5 COMPUTATIONAL STUDIES 554
PART IV NONLINEAR AND MIXED-INTEGER OPTIMIZATION
20. INTRODUCTION TO NONLINEAR AND MIXED-INTEGER OPTIMIZATION 571
20.1 MOTIVATION 571
20.2 MATHEMATICAL DESCRIPTION 575
20.3 OVERVIEW OF LOCAL OPTIMIZATION APPROACHES FOR CONVEX MINLP MODELS
576
20.4 OVERVIEW OF GLOBAL OPTIMIZATION APPROACHES FOR NONCONVEX MINLP
MODELS 579
21. THE SMIN-ABB APPROACH : THEORY AND COMPUTATIONS 587
21.1 MATHEMATICAL FORMULATION 587
21.2 GENERATION OF VALID LOWER BOUNDS 588
IMAGE 6
CONTENTS XI
21.3 GENERATION OF UPPER BOUNDS 590
21.4 SELECTION OF BRANCHING VARIABLES 591
21.5 UPDATES OF VARIABLE BOUNDS 592
21.6 THE SMIN-ABB ALGORITHM 595
21.7 COMPUTATIONAL STUDIES 598
22. THE GMIN-ABB APPROACH : THEORY AND COMPUTATIONS 617
22.1 MATHEMATICAL FORMULATION 618
22.2 GENERATION OF LOWER BOUNDS 618
22.3 GENERATION OF UPPER BOUNDS 621
22.4 SELECTION OF BRANCHING VARIABLES 622
22.5 UPDATES OF VARIABLE BOUNDS 622
22.6 THE GMIN-ABB ALGORITHM 624
22.7 COMPUTATIONAL STUDIES 624
PART V NONLINEAR CONSTRAINED SYSTEMS OF EQUATIONS
23. ALL SOLUTIONS OF NONLINEAR CONSTRAINED SYSTEMS OF EQUATIONS 641
23.1 INTRODUCTION 641
23.2 PROBLEM DEFINITION 643
23.3 CONVEX LOWER BOUNDING 646
23.4 PROCEDURE FOR ENCLOSING ALL SOLUTIONS 653
23.5 COMPUTATIONAL STUDIES 657
24. LOCATING ALL HOMOGENEOUS AZEOTROPES 667
24.1 INTRODUCTION 667
24.2 PROBLEM DESCRIPTION 668
24.3 MATHEMATICAL FORMULATION 670
24.4 ACTIVITY COEFFICIENT MODELS 672
24.5 COMPUTATIONAL STUDIES 692
REFERENCES 699
|
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| indexdate | 2024-07-09T18:35:39Z |
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| language | English |
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| physical | XVII, 739 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Floudas, Christodoulos A. 1959- Verfasser (DE-588)13590854X aut Deterministic global optimization theory, methods and applications by Christodoulos A. Floudas Dordrecht [u.a.] Kluwer 2000 XVII, 739 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 37 Mathematical optimization Nonlinear programming Deterministische Optimierung (DE-588)4149219-5 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Globale Optimierung (DE-588)4140067-7 s Deterministische Optimierung (DE-588)4149219-5 s DE-604 Nonconvex optimization and its applications 37 (DE-604)BV010085908 37 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008778545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Floudas, Christodoulos A. 1959- Deterministic global optimization theory, methods and applications Nonconvex optimization and its applications Mathematical optimization Nonlinear programming Deterministische Optimierung (DE-588)4149219-5 gnd Globale Optimierung (DE-588)4140067-7 gnd |
| subject_GND | (DE-588)4149219-5 (DE-588)4140067-7 |
| title | Deterministic global optimization theory, methods and applications |
| title_auth | Deterministic global optimization theory, methods and applications |
| title_exact_search | Deterministic global optimization theory, methods and applications |
| title_full | Deterministic global optimization theory, methods and applications by Christodoulos A. Floudas |
| title_fullStr | Deterministic global optimization theory, methods and applications by Christodoulos A. Floudas |
| title_full_unstemmed | Deterministic global optimization theory, methods and applications by Christodoulos A. Floudas |
| title_short | Deterministic global optimization |
| title_sort | deterministic global optimization theory methods and applications |
| title_sub | theory, methods and applications |
| topic | Mathematical optimization Nonlinear programming Deterministische Optimierung (DE-588)4149219-5 gnd Globale Optimierung (DE-588)4140067-7 gnd |
| topic_facet | Mathematical optimization Nonlinear programming Deterministische Optimierung Globale Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008778545&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT floudaschristodoulosa deterministicglobaloptimizationtheorymethodsandapplications |