Matrices and mathematical programming: an introduction for economists
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London u.a.
MacMillan
1981
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 236 S. graph. Darst. |
| ISBN: | 0333277686 |
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MARC
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| adam_text | Contents
Preface viii
Acknowledgements xii
Notation xiii
1 VECTORS AND MATRICES 1
1.1 Numbers and sets 1
1.2 Matrix arithmetic 5
1.3 More on multiplication 12
1.4 Vectors 16
2 LINEAR EQUATIONS 25
2.1 Gaussian elimination 25
2.2 The inverse matrix 32
2.3 Dimension 38
2.4 General systems 44
3 PIVOTING 53
3.1 Gauss Jordan pivoting 54
3.2 Tucker pivoting 57
3.3 Complementary solutions 66
4 PROJECTIONS 72
4.1 Orthogonal complements 73
4.2 Symmetric matrices 77
4.3 Least squares 82
4.4 Orthonormal bases 86
v
vi Contents
5 INTRODUCTION TO LINEAR PROGRAMMING 92
5.1 Linear programmes 93
5.2 Feasibility and solubility 98
5.3 The optimality condition 102
6 THE SIMPLEX METHOD 107
6.1 The pivot step 108
6.2 Implementation 112
6.3 Auxiliary programmes 119
7 DUALITY IN LINEAR PROGRAMMING 124
7.1 The Duality Theorem 124
7.2 Feasible bases 127
7.3 Marginal valuation 132
7.4 Strict complementarity 139
8 TOPICS IN LINEAR PROGRAMMING 142
8.1 The general case 143
8.2 The other standard form 147
8.3 Farkas Lemma 153
9 LAGRANGE MULTIPLIERS 156
9.1 Gradients 157
9.2 The Fritz John Theorem 161
9.3 The Kuhn Tucker Theorem 168
10 CONCAVE FUNCTIONS 175
10.1 Convex sets 176
10.2 Concavity 182
10.3 Quasi concavity 190
11 CONCAVE PROGRAMMING 196
11.1 Conditions for a maximum 196
11.2 Relaxing the assumptions 201
11.3 Duality 204
Appendix A: Bland s Refinement Avoids Cycling 207
Appendix B: The Marginal Value Theorem 209
Appendix C: Determinants 212
Contents vii
Appendix D: Input Output Analysis 220
Notes on Further Reading 229
References 231
Index 233
|
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| id | DE-604.BV007848060 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:10:45Z |
| institution | BVB |
| isbn | 0333277686 |
| language | English |
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| physical | XIII, 236 S. graph. Darst. |
| publishDate | 1981 |
| publishDateSearch | 1981 |
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| publisher | MacMillan |
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| spelling | Rau, Nicholas Verfasser aut Matrices and mathematical programming an introduction for economists Nicholas Rau 1. publ. London u.a. MacMillan 1981 XIII, 236 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algebra - Matrices - For economics Mathematische programmering gtt Matrices gtt Algebras, Linear Economics, Mathematical Matrices HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005175632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rau, Nicholas Matrices and mathematical programming an introduction for economists Algebra - Matrices - For economics Mathematische programmering gtt Matrices gtt Algebras, Linear Economics, Mathematical Matrices |
| title | Matrices and mathematical programming an introduction for economists |
| title_auth | Matrices and mathematical programming an introduction for economists |
| title_exact_search | Matrices and mathematical programming an introduction for economists |
| title_full | Matrices and mathematical programming an introduction for economists Nicholas Rau |
| title_fullStr | Matrices and mathematical programming an introduction for economists Nicholas Rau |
| title_full_unstemmed | Matrices and mathematical programming an introduction for economists Nicholas Rau |
| title_short | Matrices and mathematical programming |
| title_sort | matrices and mathematical programming an introduction for economists |
| title_sub | an introduction for economists |
| topic | Algebra - Matrices - For economics Mathematische programmering gtt Matrices gtt Algebras, Linear Economics, Mathematical Matrices |
| topic_facet | Algebra - Matrices - For economics Mathematische programmering Matrices Algebras, Linear Economics, Mathematical |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005175632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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