Linear programming: foundations and extensions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Kluwer Acad. Publ.
2001
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | International series in operations research & management science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 450 S. graph. Darst. |
| ISBN: | 0792373421 |
Internformat
MARC
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| 100 | 1 | |a Vanderbei, Robert J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear programming |b foundations and extensions |c Robert J. Vanderbei |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2001 | |
| 300 | |a XVIII, 450 S. |b graph. Darst. | ||
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| 490 | 0 | |a International series in operations research & management science | |
| 650 | 7 | |a Lineaire programmering |2 gtt | |
| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Mathematical optimization | |
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Datensatz im Suchindex
| _version_ | 1804128877427032064 |
|---|---|
| adam_text | Contents
Preface xiii
Preface to 2nd Edition xvii
Part 1. Basic Theory—The Simplex Method and Duality 1
Chapter 1. Introduction 3
1. Managing a Production Facility 3
2. The Linear Programming Problem 6
Exercises 8
Notes 10
Chapter 2. The Simplex Method 13
1. An Example 13
2. The Simplex Method 16
3. Initialization 19
4. Unboundedness 22
5. Geometry 22
Exercises 24
Notes 27
Chapter 3. Degeneracy 29
1. Definition of Degeneracy 29
2. Two Examples of Degenerate Problems 29
3. The Perturbation/Lexicographic Method 32
4. Bland s Rule 36
5. Fundamental Theorem of Linear Programming 38
6. Geometry 39
Exercises 42
Notes 43
Chapter 4. Efficiency of the Simplex Method 45
1. Performance Measures 45
2. Measuring the Size of a Problem 45
viii CONTENTS
3. Measuring the Effort to Solve a Problem 46
4. Worst Case Analysis of the Simplex Method 47
Exercises 52
Notes 53
Chapter 5. Duality Theory 55
1. Motivation—Finding Upper Bounds 55
2. The Dual Problem 57
3. The Weak Duality Theorem 58
4. The Strong Duality Theorem 60
5. Complementary Slackness 66
6. The Dual Simplex Method 68
7. A Dual Based Phase I Algorithm 71
8. The Dual of a Problem in General Form 73
9. Resource Allocation Problems 74
10. Lagrangian Duality 78
Exercises 79
Notes 87
Chapter 6. The Simplex Method in Matrix Notation 89
1. Matrix Notation 89
2. The Primal Simplex Method 91
3. An Example 96
4. The Dual Simplex Method 101
5. Two Phase Methods 104
6. Negative Transpose Property 105
Exercises 108
Notes 109
Chapter 7. Sensitivity and Parametric Analyses 111
1. Sensitivity Analysis 111
2. Parametric Analysis and the Homotopy Method 115
3. The Parametric Self Dual Simplex Method 119
Exercises 120
Notes 124
Chapter 8. Implementation Issues 125
1. Solving Systems of Equations: Z(/ Factorization 126
2. Exploiting Sparsity 130
3. Reusing a Factorization 136
4. Performance Tradeoffs 140
5. Updating a Factorization 141
6. Shrinking the Bump 145
CONTENTS ix
7. Partial Pricing 146
8. Steepest Edge 147
Exercises 149
Notes 150
Chapter 9. Problems in General Form 151
1. The Primal Simplex Method 151
2. The Dual Simplex Method 153
Exercises 159
Notes 160
Chapter 10. Convex Analysis 161
1. Convex Sets 161
2. Caratheodory s Theorem 163
3. The Separation Theorem 165
4. Farkas Lemma 167
5. Strict Complementarity 168
Exercises 170
Notes 171
Chapter 11. Game Theory 173
1. Matrix Games 173
2. Optimal Strategies 175
3. The Minimax Theorem 177
4. Poker 181
Exercises 184
Notes 187
Chapter 12. Regression 189
1. Measures of Mediocrity 189
2. Multidimensional Measures: Regression Analysis 191
3. L2 Regression 193
4. I*1 Regression 195
5. Iteratively Reweighted Least Squares 196
6. An Example: How Fast is the Simplex Method? 198
7. Which Variant of the Simplex Method is Best? 202
Exercises 203
Notes 208
Part 2. Network Type Problems 211
Chapter 13. Network Flow Problems 213
1. Networks 213
x CONTENTS
2. Spanning Trees and Bases 216
3. The Primal Network Simplex Method 221
4. The Dual Network Simplex Method 225
5. Putting It All Together 228
6. The Integrality Theorem 231
Exercises 232
Notes 240
Chapter 14. Applications 241
1. The Transportation Problem 241
2. The Assignment Problem 243
3. The Shortest Path Problem 244
4. Upper Bounded Network Flow Problems 247
5. The Maximum Flow Problem 250
Exercises 252
Notes 257
Chapter 15. Structural Optimization 259
1. An Example 259
2. Incidence Matrices 261
3. Stability 262
4. Conservation Laws 264
5. Minimum Weight Structural Design 267
6. Anchors Away 269
Exercises 272
Notes 272
Part 3. Interior Point Methods 275
Chapter 16. The Central Path 277
Warning: Nonstandard Notation Ahead 277
1. The Barrier Problem 277
2. Lagrange Multipliers 280
3. Lagrange Multipliers Applied to the Barrier Problem 283
4. Second Order Information 285
5. Existence 285
Exercises 287
Notes 289
Chapter 17. A Path Following Method 291
1. Computing Step Directions 291
2. Newton s Method 293
3. Estimating an Appropriate Value for the Barrier Parameter 294
CONTENTS xi
4. Choosing the Step Length Parameter 295
5. Convergence Analysis 296
Exercises 302
Notes 306
Chapter 18. The KKT System 307
1. The Reduced KKT System 307
2. The Normal Equations 308
3. Step Direction Decomposition 310
Exercises 313
Notes 313
Chapter 19. Implementation Issues 315
1. Factoring Positive Definite Matrices 315
2. Quasidefinite Matrices 319
3. Problems in General Form 325
Exercises 331
Notes 331
Chapter 20. The Affine Scaling Method 333
1. The Steepest Ascent Direction 333
2. The Projected Gradient Direction 335
3. The Projected Gradient Direction with Scaling 337
4. Convergence 341
5. Feasibility Direction 343
6. Problems in Standard Form 344
Exercises 345
Notes 346
Chapter 21. The Homogeneous Self Dual Method 349
1. From Standard Form to Self Dual Form 349
2. Homogeneous Self Dual Problems 350
3. Back to Standard Form 360
4. Simplex Method vs Interior Point Methods 363
Exercises 367
Notes 368
Part 4. Extensions 371
Chapter 22. Integer Programming 373
1. Scheduling Problems 373
2. The Traveling Salesman Problem 375
3. Fixed Costs 378
xii CONTENTS
4. Nonlinear Objective Functions 378
5. Branch and Bound 380
Exercises 392
Notes 393
Chapter 23. Quadratic Programming 395
1. The Markowitz Model 395
2. The Dual 399
3. Convexity and Complexity 402
4. Solution Via Interior Point Methods 404
5. Practical Considerations 406
Exercises 409
Notes 411
Chapter 24. Convex Programming 413
1. Differentiable Functions and Taylor Approximations 413
2. Convex and Concave Functions 414
3. Problem Formulation 414
4. Solution Via Interior Point Methods 415
5. Successive Quadratic Approximations 417
6. Merit Functions 417
7. Parting Words 421
Exercises 421
Notes 423
Appendix A. Source Listings 425
1. The Self Dual Simplex Method 426
2. The Homogeneous Self Dual Method 429
Answers to Selected Exercises 433
Bibliography 435
Index 443
|
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| dewey-full | 519.7/2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.7/2 |
| dewey-search | 519.7/2 |
| dewey-sort | 3519.7 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| spelling | Vanderbei, Robert J. Verfasser aut Linear programming foundations and extensions Robert J. Vanderbei 2. ed. Boston [u.a.] Kluwer Acad. Publ. 2001 XVIII, 450 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series in operations research & management science Lineaire programmering gtt Wiskundige methoden gtt Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Innere-Punkte-Methode (DE-588)4352322-5 gnd rswk-swf Netzwerkfluss (DE-588)4126130-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Lineare Optimierung (DE-588)4035816-1 s Innere-Punkte-Methode (DE-588)4352322-5 s 2\p DE-604 Netzwerkfluss (DE-588)4126130-6 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009599086&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Vanderbei, Robert J. Linear programming foundations and extensions Lineaire programmering gtt Wiskundige methoden gtt Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd Innere-Punkte-Methode (DE-588)4352322-5 gnd Netzwerkfluss (DE-588)4126130-6 gnd |
| subject_GND | (DE-588)4035816-1 (DE-588)4352322-5 (DE-588)4126130-6 (DE-588)4151278-9 |
| title | Linear programming foundations and extensions |
| title_auth | Linear programming foundations and extensions |
| title_exact_search | Linear programming foundations and extensions |
| title_full | Linear programming foundations and extensions Robert J. Vanderbei |
| title_fullStr | Linear programming foundations and extensions Robert J. Vanderbei |
| title_full_unstemmed | Linear programming foundations and extensions Robert J. Vanderbei |
| title_short | Linear programming |
| title_sort | linear programming foundations and extensions |
| title_sub | foundations and extensions |
| topic | Lineaire programmering gtt Wiskundige methoden gtt Linear programming Mathematical optimization Lineare Optimierung (DE-588)4035816-1 gnd Innere-Punkte-Methode (DE-588)4352322-5 gnd Netzwerkfluss (DE-588)4126130-6 gnd |
| topic_facet | Lineaire programmering Wiskundige methoden Linear programming Mathematical optimization Lineare Optimierung Innere-Punkte-Methode Netzwerkfluss Einführung |
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