Integer and combinatorial optimization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Chichester ; Weinheim ; Brisbane ; Singapore ; Toronto
John Wiley & Sons, inc
[1999]
|
| Series: | Wiley-Interscience series in discrete mathematics and optimization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xiv, 763 Seiten Illustrationen |
| ISBN: | 0471359432 047182819X 9780471359432 9781118627259 |
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MARC
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| 245 | 1 | 0 | |a Integer and combinatorial optimization |c George Nemhauser (School of Industrial and Systems Engineering Georgia Institute of Technology, Atlanta, Georigia), Laurence A. Wolsey (Center for Operations Research and Econometrics Unversité Catholique de Louvain, Louvain-la-Neuve, Belgien) |
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Record in the Search Index
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| adam_text | Contents PARTI. 1.1 The Scope of Integer and Combinatorial Optimization 1. 2. 3. 4. 5. 6. 7. 8. 1.2 Introduction Duality The Primal and Dual Simplex Algorithms Subgradient Optimization Notes Graphs and Networks 1. 2. 3. 4. 5. 6. 7. 1.4 Introduction Modeling with Binary Variables I: Knapsack, Assignment and Matching, Covering, Packing and Partitioning 5 Modeling with Binary Variables II: Facility Location, Fixed-Charge Network Flow, and Traveling Salesman 7 Modeling with Binary Variables III: Nonlinear Functions and Disjunctive Constraints Choices in Model Formulation Preprocessing Notes Exercises Linear Programming 1. 2. 3. 4. 5. 13 FOUNDATIONS Introduction The Minimum-Weight or Shortest-Path Problem The Minimum-Weight Spanning Tree Problem The Maximum-Flow and Minimum-Cut Problems The Transportation Problem: A Primal-Dual Algorithm A Primal Simplex Algorithm for Network Flow Problems Notes Polyhedral Theory 1. 2. 3. 4. 5. Introduction and Elementary Linear Algebra Definitions ofPolyhedra and Dimension Describing Polyhedra by Facets Describing Polyhedra by Extreme Points and Extreme Rays Polarity 1 3 3 10 14 17 20 22 27 27 28 30 41 49 50 50 55 60 62 68 76 82 83 83 85 88 92 98 xi
Contents xii 6. 7. 8. 1.5 1.6 114 1. 2. 3. 4. 5. 6. 7. 8. 9. 114 117 121 125 127 131 139 142 143 Introduction Measuring Algorithm Efficiency and Problem Complexity Some Problems Solvable in Polynomial Time Remarks on 0-1 and Pure-Integer Programming Nondeterministic Polynomial-Time Algorithms and A՞^ Problems The Most Difficult.W Problems: The Class Я^ Complexity and Polyhedra Notes Exercises Polynomial-Time Algorithmsfor Linear Programming Introduction The Ellipsoid Algorithm The Polynomial Equivalence of Separation and Optimization A Projective Algorithm A Strongly Polynomial Algorithm for Combinatorial Linear Programs Notes Integer Lattices 1. 2. 3. 4. 5. 6. 7. Introduction The Euclidean Algorithm Continued Fractions Lattices and Hermite Normal Form Reduced Bases Notes Exercises PARTII. П.1 104 109 109 Computational Complexity 1. 2. 3. 4. 5. 6. 1.7 Polyhedral Ties BetweenLinear and Integer Programs Notes Exercises GENERAL INTEGER PROGRAMMING 146 146 147 161 164 172 180 182 182 184 187 189 195 201 202 203 The Theory of Valid Inequalities 205 1. Introduction 2. Generating All Valid Inequalities 3. Gomory’s Fractional Cuts and Rounding 4. Superadditive Functions and Valid Inequalities 5. A Polyhedral Description of Superadditive Valid Inequalities for Independence Systems 6. Valid Inequalities for Mixed-Integer Sets 7. Superadditivity for Mixed-Integer Sets 8. Notes 9. Exercises 205 217 227 229 237 242 246 254 256
Contents xiii II.2 Strong Valid Inequalities and Facets for Structured Integer Programs II.3 1. Introduction 2. Valid Inequalities for the 0-1 Knapsack Polytope 3. Valid Inequalities for the Symmetric Traveling Salesman Polytope 4. Valid Inequalities for Variable Upper-Bound Flow Models 5. Notes 6. Exercises 259 265 270 281 290 291 Duality and Relaxation 296 1. 2. 3. 4. 5. 6. 7. 8. 9. II.4 II.5 Introduction Duality and the Value Function Superadditive Duality The Maximum-Weight Path Formulation and Superadditive Duality Modular Arithmetic and the Group Problem Lagrangian Relaxation and Duality Benders’ Reformulation Notes Exercises 296 300 304 308 312 323 337 341 343 General Algorithms 349 1. Introduction 2. Branch-and-Bound Using Linear Programming Relaxations 3. General Cutting-Plane Algorithms 4. Notes 5. Exercises 349 355 367 379 381 Special-Purpose Algorithms 383 1. 2. 3. 4. 5. 6. 7. II.6 259 Introduction A Cutting-Plane Algorithm Using Strong Valid Inequalities Primal and Dual Heuristic Algorithms Decomposition Algorithms Dynamic Programming Notes Exercises Applicationsof Special-Purpose Algorithms 1. 2. 3. 4. 5. 6. 7. Knapsack and Group Problems 0-1 Integer Programming Problems The Symmetric Traveling Salesman Problem Fixed-Charge Network Flow Problems Applications of Basis Reduction Notes Exercises 383 386 393 409 417 424 427 433 433 456 469 495 513 520 526
xiv Contents PARTIIL COMBINATORIAL OPTIMIZATION IILI Integral Polyhedra 1. 2. 3. 4. 5. 6. 7. 8. IIL2 IIL3 Introduction Totally Unimodular Matrices Network Matrices Balanced and Totally Balanced Matrices Node Packing and Perfect Graphs Blocking and Integral Polyhedra Notes Exercises 533 535 535 540 546 562 573 586 598 602 Matching 608 1. Introduction 2. Maximum-Cardinality Matching 3. Maximum-Weight Matching 4. Additional Results on Matching and Related Problems 5. Notes 6. Exercises 608 611 627 636 654 655 Matroid and Submodular Function Optimization 659 1, 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Introduction Elementary Properties Maximum-Weight Independent Sets Matroid Intersection Weighted Matroid Intersection Polymatroids, Separation, and Submodular Function Minimization Algorithms To Minimize a Submodular Function Covering with Independent Sets and Matroid Partition Submodular Function Maximization Notes Exercises 659 662 666 671 678 688 694 702 708 712 714 References 721 Author Index 749 Subject Index 755
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| any_adam_object | 1 |
| author | Nemhauser, George L. 1937- Wolsey, Laurence A. 1945- |
| author_GND | (DE-588)11091340X (DE-588)129756326 |
| author_facet | Nemhauser, George L. 1937- Wolsey, Laurence A. 1945- |
| author_role | aut aut |
| author_sort | Nemhauser, George L. 1937- |
| author_variant | g l n gl gln l a w la law |
| building | Verbundindex |
| bvnumber | BV012976379 |
| classification_rvk | SK 890 QH 422 QH 425 |
| classification_tum | MAT 913f MAT 052f |
| ctrlnum | (OCoLC)264955753 (DE-599)BVBBV012976379 |
| dewey-full | 519.77 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.77 |
| dewey-search | 519.77 |
| dewey-sort | 3519.77 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| indexdate | 2025-02-20T06:37:31Z |
| institution | BVB |
| isbn | 0471359432 047182819X 9780471359432 9781118627259 |
| language | English |
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| physical | xiv, 763 Seiten Illustrationen |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | John Wiley & Sons, inc |
| record_format | marc |
| series2 | Wiley-Interscience series in discrete mathematics and optimization |
| spellingShingle | Nemhauser, George L. 1937- Wolsey, Laurence A. 1945- Integer and combinatorial optimization Combinatorial optimization Integer programming Kombinatorische Optimierung (DE-588)4031826-6 gnd Diskrete Optimierung (DE-588)4150179-2 gnd Ganzzahlige Optimierung (DE-588)4155950-2 gnd |
| subject_GND | (DE-588)4031826-6 (DE-588)4150179-2 (DE-588)4155950-2 |
| title | Integer and combinatorial optimization |
| title_auth | Integer and combinatorial optimization |
| title_exact_search | Integer and combinatorial optimization |
| title_full | Integer and combinatorial optimization George Nemhauser (School of Industrial and Systems Engineering Georgia Institute of Technology, Atlanta, Georigia), Laurence A. Wolsey (Center for Operations Research and Econometrics Unversité Catholique de Louvain, Louvain-la-Neuve, Belgien) |
| title_fullStr | Integer and combinatorial optimization George Nemhauser (School of Industrial and Systems Engineering Georgia Institute of Technology, Atlanta, Georigia), Laurence A. Wolsey (Center for Operations Research and Econometrics Unversité Catholique de Louvain, Louvain-la-Neuve, Belgien) |
| title_full_unstemmed | Integer and combinatorial optimization George Nemhauser (School of Industrial and Systems Engineering Georgia Institute of Technology, Atlanta, Georigia), Laurence A. Wolsey (Center for Operations Research and Econometrics Unversité Catholique de Louvain, Louvain-la-Neuve, Belgien) |
| title_short | Integer and combinatorial optimization |
| title_sort | integer and combinatorial optimization |
| topic | Combinatorial optimization Integer programming Kombinatorische Optimierung (DE-588)4031826-6 gnd Diskrete Optimierung (DE-588)4150179-2 gnd Ganzzahlige Optimierung (DE-588)4155950-2 gnd |
| topic_facet | Combinatorial optimization Integer programming Kombinatorische Optimierung Diskrete Optimierung Ganzzahlige Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008840691&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nemhausergeorgel integerandcombinatorialoptimization AT wolseylaurencea integerandcombinatorialoptimization |
Indexes
THWS Würzburg Zentralbibliothek Lesesaal
| Call Number: |
1000 SK 890 N433 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |