Introduction to linear programming: applications and extensions
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Dekker
1991
|
| Schriftenreihe: | Pure and applied mathematics
141 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 353 S. graph. Darst. |
| ISBN: | 0824783832 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to linear programming |b applications and extensions |c Richard B. Darst |
| 264 | 1 | |a New York u.a. |b Dekker |c 1991 | |
| 300 | |a XII, 353 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied mathematics |v 141 | |
| 650 | 7 | |a Programmation linéaire |2 ram | |
| 650 | 4 | |a Linear programming | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface v
Chapter 1. Introduction to Systems of Linear Equations (Linear
Systems) and Related Properties of Matrices 1
1.1 Linear Systems 1
1.2 Row Echelon Algorithm 4
1.3 Row Reduction 6
1.4 Matrix Operations 9
1.5 Rank 13
1.6 Identity and Inverse Matrices 13
1.7 Linear Independence 16
1.8 Rearrangement 19
1.9 Solutions to Linear Systems 20
Exercises 21
Chapter 2. Introduction to Linear Programming 24
2.1 Example 2.1: A Production Problem 26
2.2 Example 2.2: A Diet Problem 34
2.3 Example 2.3: A Transportation Problem 36
2.4 Duality 38
ix
x Contents
2.5 Two Fundamental Facts About Standard and
Symmetric Primal Dual Pairs 44
Exercises 44
Chapter 3. Elementary Properties of the Feasible Set for an LP 64
3.1 Basic Properties 64
3.2 Basic Feasible Solutions 69
3.3 The Fundamental Theorem of Linear
Programming 72
Exercises 73
Chapter 4. Introduction to the Simplex Method 80
4.1 Notation 80
4.2 Pertinent Algebra 81
4.3 The Simplex Tableau 82
4.4 Reduced Costs 83
4.5 Conditions for Optimality 84
4.6 The Objective Function 86
4.7 Simplex Method Pivoting 89
4.8 When No Optimal Solution Exists 94
4.9 Multiple Solutions 96
4.10 Degeneracy 97
4.11 Phase 1 99
4.12 The Revised Simplex Method 101
Exercises 104
Chapter 5. Topics in LP and Extensions 114
5.1 Examples that Fit into LP Format 115
5.2 Infeasibility 118
5.3 Multiperiod Problems 119
5.4 More Objectives 122
5.5 Integer Variables 126
5.6 Transportation Problems 130
5.7 Introduction to Networks 131
5.8 Introduction to Dynamic Programming 147
5.9 Stability and Sensitivity 156
Exercises 165
Chapter 6. Duality 202
6.1 The Duality Theorem of Linear Programming 202
6.2 Complementary Slackness 203
Contents xi
6.3 Kuhn Tucker Conditions 205
Exercises 207
Chapter 7. Quadratic Programming 208
7.1 Quadratic Functions 209
7.2 Convex Quadratic Functions 217
7.3 Kuhn Tucker Conditions for Convex Quadratic
Programs 218
7.4 Linear Complementarity Formulation of Kuhn
Tucker Conditions 219
7.5 Investment Application 221
Exercises 224
Chapter 8. Minimizing a Quadratic Function 226
8.1 Eigenvalue Conditions for Positive
(Semi)definiteness 227
8.2 Newton s Method 228
8.3 Steepest Descent 230
8.4 Conjugate Directions 236
8.5 Conjugate Gradient Method 239
8.6 Conjugate Gradient Algorithm 243
Exercises 244
Chapter 9. Network Algorithms 246
9.1 Notation 247
9.2 Project Planning 247
9.3 Longest Path Algorithm 248
9.4 Shortest Path Algorithm 251
9.5 Minimum Spanning Tree Algorithm 255
9.6 Maximum (Simple) Path Flow Algorithm 256
9.7 Residual Digraph 258
9.8 Maximum Flow Algorithm 259
9.9 Minimum Cost Maximum Flows:
Transportation and Assignment
Problems 264
9.10 Minimum Cost Maximum Flow Algorithm 269
Exercises 270
Appendix 1. Forms of LPs 273
xii Contents
Appendix 2. Solutions Supplement for Chapter 2 278
Appendix 3. Solutions Supplement for Chapter 5 315
Reading List 346
Index 348
|
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| id | DE-604.BV004638296 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:15:22Z |
| institution | BVB |
| isbn | 0824783832 |
| language | English |
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| physical | XII, 353 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Darst, Richard B. Verfasser aut Introduction to linear programming applications and extensions Richard B. Darst New York u.a. Dekker 1991 XII, 353 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 141 Programmation linéaire ram Linear programming Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s DE-604 Pure and applied mathematics 141 (DE-604)BV000001885 141 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002847261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Darst, Richard B. Introduction to linear programming applications and extensions Pure and applied mathematics Programmation linéaire ram Linear programming Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | Introduction to linear programming applications and extensions |
| title_auth | Introduction to linear programming applications and extensions |
| title_exact_search | Introduction to linear programming applications and extensions |
| title_full | Introduction to linear programming applications and extensions Richard B. Darst |
| title_fullStr | Introduction to linear programming applications and extensions Richard B. Darst |
| title_full_unstemmed | Introduction to linear programming applications and extensions Richard B. Darst |
| title_short | Introduction to linear programming |
| title_sort | introduction to linear programming applications and extensions |
| title_sub | applications and extensions |
| topic | Programmation linéaire ram Linear programming Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Programmation linéaire Linear programming Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002847261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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