Discrete optimization:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2005
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Handbooks in operations research and management science
12 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 607 S. graph. Darst., Kt. |
| ISBN: | 0444515070 9780444515070 |
Internformat
MARC
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| 245 | 1 | 0 | |a Discrete optimization |c ed. by K. Aardal ... |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2005 | |
| 300 | |a XI, 607 S. |b graph. Darst., Kt. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Handbooks in operations research and management science |v 12 | |
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| 650 | 4 | |a Programmation en nombres entiers | |
| 650 | 4 | |a Integer programming | |
| 650 | 4 | |a Mathematical optimization | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
PREFACE ix
CHAPTER 1
On the History of Combinatorial Optimization (Till 1960)
Alexander Schrijver 1
1 Introduction 1
2 The assignment problem 2
3 The transportation problem 13
4 Menger s theorem and maximum flow 26
5 Shortest spanning tree 34
6 Shortest path 40
7 The traveling salesman problem 48
References 59
CHAPTER 2
Computational Integer Programming and Cutting Planes
Armin Fugenschuh and Alexander Martin 69
1 Introduction 69
2 Formulations and structure analysis 71
3 Relaxations 79
4 Branch and bound strategies 105
5 Final remarks 115
References 117
CHAPTER 3
The Structure of Group Relaxations
Rekha R. Thomas 123
1 Introduction 123
2 Group relaxations 126
3 Associated sets 136
4 Arithmetic degree 143
5 The Chain theorem 150
6 Gomory integer programs 154
v
vi Contents
7 Gomory families and Hilbert bases 157
8 Algebraic notes 165
References 168
CHAPTER 4
Integer Programming, Lattices, and Results in Fixed Dimension
Karen Aardal and Friedrich Eisenbrand 171
1 Introduction 171
2 Notation and basic definitions 172
3 Lattice basis reduction 176
4 Algorithms for the integer feasibility problem in fixed dimension 195
5 Algorithms for the integer optimization problem in fixed dimension 209
6 Using lattices to reformulate the problem 218
7 Integer hulls and cutting plane closures in fixed dimension 228
References 239
CHAPTER 5
Primal Integer Programming
Bianca Spille and Robert Weismantel 245
1 Introduction 245
2 Efficient primal algorithms 247
3 Irreducibility and integral generating sets 252
4 General integer programming algorithms 258
5 Combinatorial optimization 268
References 274
CHAPTER 6
Balanced Matrices
Michele Conforti and Gerard Cornuejols 277
1 Introduction 277
2 Integral polytopes 278
3 Bicoloring 280
4 Total dual integrality 282
5 Ar Balanced matrices 285
6 Perfection and idealness 289
7 Propositional logic 291
8 Nonlinear 0,1 optimization 294
9 Balanced hypergraphs 294
10 Bipartite representation 298
11 Totally balanced 0,1 matrices 298
12 Signing 0,1 matrices 300
Contents vii
13 Truemper s theorem 301
14 Decomposition theorem 304
15 Recognition algorithm 310
16 More decomposition theorems 313
17 Some conjectures and open questions 315
References 317
CHAPTER 7
Submodular Function Minimization
S. Thomas McCormick 321
1 Introduction 321
2 Building blocks for SFM algorithms 329
3 The SFM algorithms 345
4 Comparing and contrasting the algorithms 378
5 Solvable extensions of SFM 382
6 Future directions for SFM algorithms 386
References 388
CHAPTER 8
Semidefinite Programming and Integer Programming
Monique Laurent and Franz Rendl 393
1 Introduction 393
2 Semidefinite programming: duality, algorithms,
complexity, and geometry 394
3 Semidefinite programming and integer 0/1 programming 408
4 Semidefinite relaxation for the maximum stable set problem 431
5 Semidefinite relaxation for the max cut problem 441
6 Applications of semidefinite programming and the rounding
hyperplane technique to other combinatorial optimization problems 452
7 Further topics 485
8 Semidefinite programming and the quadratic assignment problem 493
9 Epilogue: semidefinite programming and algebraic connectivity 500
10 Appendix: surveys, books and software 502
References 504
CHAPTER 9
Algorithms for Stochastic Mixed Integer
Programming Models
Suvrajeet Sen 515
1 Introduction 515
2 Preliminaries for decomposition algorithms 518
viii Contents
3 Decomposition algorithms for two stage SMIP:
stagewise decomposition 527
4 Decomposition algorithms for multi stage SMIP:
scenario decomposition 547
5 Conclusions 554
References 555
CHAPTER 10
Constraint Programming
Alexander Bockmayr and John N. Hooker 559
1 Introduction 559
2 Constraints 567
3 Search 578
4 Hybrid methods 583
References 593
Subject Index 601
|
| adam_txt |
Contents
PREFACE ix
CHAPTER 1
On the History of Combinatorial Optimization (Till 1960)
Alexander Schrijver 1
1 Introduction 1
2 The assignment problem 2
3 The transportation problem 13
4 Menger's theorem and maximum flow 26
5 Shortest spanning tree 34
6 Shortest path 40
7 The traveling salesman problem 48
References 59
CHAPTER 2
Computational Integer Programming and Cutting Planes
Armin Fugenschuh and Alexander Martin 69
1 Introduction 69
2 Formulations and structure analysis 71
3 Relaxations 79
4 Branch and bound strategies 105
5 Final remarks 115
References 117
CHAPTER 3
The Structure of Group Relaxations
Rekha R. Thomas 123
1 Introduction 123
2 Group relaxations 126
3 Associated sets 136
4 Arithmetic degree 143
5 The Chain theorem 150
6 Gomory integer programs 154
v
vi Contents
7 Gomory families and Hilbert bases 157
8 Algebraic notes 165
References 168
CHAPTER 4
Integer Programming, Lattices, and Results in Fixed Dimension
Karen Aardal and Friedrich Eisenbrand 171
1 Introduction 171
2 Notation and basic definitions 172
3 Lattice basis reduction 176
4 Algorithms for the integer feasibility problem in fixed dimension 195
5 Algorithms for the integer optimization problem in fixed dimension 209
6 Using lattices to reformulate the problem 218
7 Integer hulls and cutting plane closures in fixed dimension 228
References 239
CHAPTER 5
Primal Integer Programming
Bianca Spille and Robert Weismantel 245
1 Introduction 245
2 Efficient primal algorithms 247
3 Irreducibility and integral generating sets 252
4 General integer programming algorithms 258
5 Combinatorial optimization 268
References 274
CHAPTER 6
Balanced Matrices
Michele Conforti and Gerard Cornuejols 277
1 Introduction 277
2 Integral polytopes 278
3 Bicoloring 280
4 Total dual integrality 282
5 Ar Balanced matrices 285
6 Perfection and idealness 289
7 Propositional logic 291
8 Nonlinear 0,1 optimization 294
9 Balanced hypergraphs 294
10 Bipartite representation 298
11 Totally balanced 0,1 matrices 298
12 Signing 0,1 matrices 300
Contents vii
13 Truemper's theorem 301
14 Decomposition theorem 304
15 Recognition algorithm 310
16 More decomposition theorems 313
17 Some conjectures and open questions 315
References 317
CHAPTER 7
Submodular Function Minimization
S. Thomas McCormick 321
1 Introduction 321
2 Building blocks for SFM algorithms 329
3 The SFM algorithms 345
4 Comparing and contrasting the algorithms 378
5 Solvable extensions of SFM 382
6 Future directions for SFM algorithms 386
References 388
CHAPTER 8
Semidefinite Programming and Integer Programming
Monique Laurent and Franz Rendl 393
1 Introduction 393
2 Semidefinite programming: duality, algorithms,
complexity, and geometry 394
3 Semidefinite programming and integer 0/1 programming 408
4 Semidefinite relaxation for the maximum stable set problem 431
5 Semidefinite relaxation for the max cut problem 441
6 Applications of semidefinite programming and the rounding
hyperplane technique to other combinatorial optimization problems 452
7 Further topics 485
8 Semidefinite programming and the quadratic assignment problem 493
9 Epilogue: semidefinite programming and algebraic connectivity 500
10 Appendix: surveys, books and software 502
References 504
CHAPTER 9
Algorithms for Stochastic Mixed Integer
Programming Models
Suvrajeet Sen 515
1 Introduction 515
2 Preliminaries for decomposition algorithms 518
viii Contents
3 Decomposition algorithms for two stage SMIP:
stagewise decomposition 527
4 Decomposition algorithms for multi stage SMIP:
scenario decomposition 547
5 Conclusions 554
References 555
CHAPTER 10
Constraint Programming
Alexander Bockmayr and John N. Hooker 559
1 Introduction 559
2 Constraints 567
3 Search 578
4 Hybrid methods 583
References 593
Subject Index 601 |
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| spelling | Discrete optimization ed. by K. Aardal ... 1. ed. Amsterdam [u.a.] Elsevier 2005 XI, 607 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Handbooks in operations research and management science 12 Optimisation mathématique Programmation en nombres entiers Integer programming Mathematical optimization Diskrete Optimierung (DE-588)4150179-2 gnd rswk-swf Diskrete Optimierung (DE-588)4150179-2 s DE-604 Aardal, Karen 1961- Sonstige (DE-588)122921682 oth Handbooks in operations research and management science 12 (DE-604)BV002805695 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014605739&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Discrete optimization Handbooks in operations research and management science Optimisation mathématique Programmation en nombres entiers Integer programming Mathematical optimization Diskrete Optimierung (DE-588)4150179-2 gnd |
| subject_GND | (DE-588)4150179-2 |
| title | Discrete optimization |
| title_auth | Discrete optimization |
| title_exact_search | Discrete optimization |
| title_exact_search_txtP | Discrete optimization |
| title_full | Discrete optimization ed. by K. Aardal ... |
| title_fullStr | Discrete optimization ed. by K. Aardal ... |
| title_full_unstemmed | Discrete optimization ed. by K. Aardal ... |
| title_short | Discrete optimization |
| title_sort | discrete optimization |
| topic | Optimisation mathématique Programmation en nombres entiers Integer programming Mathematical optimization Diskrete Optimierung (DE-588)4150179-2 gnd |
| topic_facet | Optimisation mathématique Programmation en nombres entiers Integer programming Mathematical optimization Diskrete Optimierung |
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