Advanced linear-programming computing techniques:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1968
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 341 - 347 |
| Beschreibung: | XI, 355 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Advanced linear-programming computing techniques |c William Orchard-Hays |
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1968 | |
| 300 | |a XI, 355 S. | ||
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| 500 | |a Literaturverz. S. 341 - 347 | ||
| 650 | 4 | |a Programmation linéaire | |
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| 650 | 7 | |a algorithme paramétrique |2 inriac | |
| 650 | 7 | |a algorithme simplexe |2 inriac | |
| 650 | 7 | |a dualité |2 inriac | |
| 650 | 7 | |a méthode décomposition |2 inriac | |
| 650 | 7 | |a programmation linéaire |2 inriac | |
| 650 | 4 | |a Linear programming | |
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Datensatz im Suchindex
| _version_ | 1804116735455920128 |
|---|---|
| adam_text | CONTENTS
PREFACE vii
1. INTRODUCTION 1
1.1 Theory and Practice 1
1.2 Notation 3
1.3 Classical Statement of Problem and Duality Theorem 5
1.4 Background on Computer Codes 7
2. GENERALIZED PROBLEM STATEMENT 11
2.1 Linear Equations: Standard Form 11
2.2 Categorization of Variables: Ranges 12
2.3 Duality Theorem: Range Transforms 18
2.4 Data Formats for Computer Programs 20
3. THE SIMPLEX METHOD 23
3.1 Concept of a Basis 23
3.2 Basic Theorems 27
3.3 Obtaining Feasibility 43
3.4 The Composite Primal Algorithm 47
3.5 Illustrative Examples 50
4. THE PRODUCT FORM OF INVERSE 63
4.1 Elementary Column and Row Matrices 64
4.2 Forward Transformation of Columns 70
4.3 Backward Transformation of Rows 71
4.4 Reinversion Techniques 73
5. DUAL PROBLEMS 83
5.1 Proof of the Duality Theorem and Its Corollaries 83
5.2 The Dual Algorithm 88
5.3 Dualization of a Problem 95
5.4 Interpretation of Results 99
6. PRICING AND PIVOT SELECTION 109
6.1 Multiple and Partial Pricing 109
6.2 Tiebreaking and Secondary Pivot Selection 114
6.3 Scaling and Digital Stability 122
6.4 Tolerances 127
6.5 Crashing Techniques 131
IX
X CONTENTS
7. RANGING PROCEDURES 141
7.1 Right hand side Elements 142
7.2 Objective Coefficients 143
7.3 Variables 146
7.4 Structural Coefficients 154
8. PARAMETRIC ALGORITHMS 163
8.1 Parameterizing the Right hand Side 164
8.2 Parameterizing the Objective Function 169
8.3 Parameterizing the Rim of the Problem 171
8.4 Parameterizing a Structural Column 177
8.5 Parameterizing a Structural Row 187
8.6 Generalization of Structural Parameterization 200
9. EXTENSIONS TO THE PRIMAL ALGORITHM 205
9.1 Separable Programming 205
9.2 Generalized Upper Bounding: Group Problems 209
9.3 Transportation Problems as Group Problems 221
9.4 Integer Programming Problems 224
9.5 A Parametric Algorithm 227
9.6 Process control Optimization 229
10. DECOMPOSITION TECHNIQUES 239
10.1 Background 239
10.2 Form of the Problem 240
10.3 The Dantzig Wolfe Algorithm 242
10.4 Specializations and Generalizations of the
Dantzig Wolfe Algorithm 249
10.5 Rosen s Algorithm 256
10.6 Decomposition Applied to Multiplant and Multitime
Period Models 260
11. A UNIFIED APPROACH TO GENERALIZED DECOMPOSITION 263
12. A PARAMETRIC DECOMPOSITION ALGORITHM AND
BLOCK PRODUCT FORM OF INVERSE 271
12.1 Conceptual Overview: Phase 1 271
12.2 The Form of the Basis in Phase 2 273
12.3 Simplified Structure and Notation 276
12.4 The PARRHS Algorithm in Block Form 277
12.5 The Three Primary Cases with Proofs 280
12.6 The Secondary Cases with Proofs 284
12.7 Reinverting and Restarting 291
12.8 Summary and Relation to Other Methods 293
13. SOLUTION STRATEGY AND AUXILIARY CONTROLS 297
13.1 Classification of Auxiliary Controls for LP Problems 297
13.2 Demand Actions for Off normal Conditions 300
13.3 Typical First Procedures for New Models 303
13.4 Initial Postoptimal Runs 304
CONTENTS XI
13.5 Mapping Solution Space; Trees of Solutions 305
13.6 Solution Strategy in Nonstandard LP 306
APPENDIX A. ELEMENTARY TRANSFORMATIONS 309
APPENDIX B. DESIGN CRITERIA FOR A COMPLETE
MATHEMATICAL PROGRAMMING SYSTEM 321
APPENDIX C. SELECTED BIBLIOGRAPHY 341
INDEX 349
|
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| author | Orchard-Hays, William |
| author_facet | Orchard-Hays, William |
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| author_sort | Orchard-Hays, William |
| author_variant | w o h woh |
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| bvnumber | BV002277452 |
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| ctrlnum | (OCoLC)179993 (DE-599)BVBBV002277452 |
| dewey-full | 519.92 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.92 |
| dewey-search | 519.92 |
| dewey-sort | 3519.92 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV002277452 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:43:14Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001496274 |
| oclc_num | 179993 |
| open_access_boolean | |
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| physical | XI, 355 S. |
| psigel | HUB-ZB011201011 |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | McGraw-Hill |
| record_format | marc |
| spelling | Orchard-Hays, William Verfasser aut Advanced linear-programming computing techniques William Orchard-Hays New York [u.a.] McGraw-Hill 1968 XI, 355 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 341 - 347 Programmation linéaire Programmation linéaire ram algorithme paramétrique inriac algorithme simplexe inriac dualité inriac méthode décomposition inriac programmation linéaire inriac Linear programming Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Programmierung (DE-588)4076370-5 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001496274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orchard-Hays, William Advanced linear-programming computing techniques Programmation linéaire Programmation linéaire ram algorithme paramétrique inriac algorithme simplexe inriac dualité inriac méthode décomposition inriac programmation linéaire inriac Linear programming Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Programmierung (DE-588)4076370-5 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4035816-1 (DE-588)4076370-5 |
| title | Advanced linear-programming computing techniques |
| title_auth | Advanced linear-programming computing techniques |
| title_exact_search | Advanced linear-programming computing techniques |
| title_full | Advanced linear-programming computing techniques William Orchard-Hays |
| title_fullStr | Advanced linear-programming computing techniques William Orchard-Hays |
| title_full_unstemmed | Advanced linear-programming computing techniques William Orchard-Hays |
| title_short | Advanced linear-programming computing techniques |
| title_sort | advanced linear programming computing techniques |
| topic | Programmation linéaire Programmation linéaire ram algorithme paramétrique inriac algorithme simplexe inriac dualité inriac méthode décomposition inriac programmation linéaire inriac Linear programming Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Optimierung (DE-588)4035816-1 gnd Programmierung (DE-588)4076370-5 gnd |
| topic_facet | Programmation linéaire algorithme paramétrique algorithme simplexe dualité méthode décomposition programmation linéaire Linear programming Numerisches Verfahren Lineare Optimierung Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001496274&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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