Linear semi-infinite optimization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
1998
|
| Series: | Mathematical methods in practice
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 343 S. graph. Darst. |
| ISBN: | 0471970409 |
Staff View
MARC
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| 100 | 1 | |a Goberna, Miguel Á. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Linear semi-infinite optimization |c Miguel A. Goberna and Marco A. López |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 1998 | |
| 300 | |a XII, 343 S. |b graph. Darst. | ||
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| 650 | 7 | |a problème primal |2 inriac | |
| 650 | 7 | |a programmation linéaire |2 inriac | |
| 650 | 4 | |a Duality theory (Mathematics) | |
| 650 | 4 | |a Mathematical optimization | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Part I: Modelling 1
1 Modelling with the Primal Problem 3
1.1 The primal LSIP problem 3
1.2 Approximation 6
1.3 Separation of sets in pattern recognition 13
1.4 Environmental policies 16
1.5 Generalized Neyman Pearson problem for grouped data 18
1.6 Optimal experimental design in regression 20
1.7 Constrained multinomial maximum likelihood estimation 28
1.8 Mathematical programming 31
Exercises 37
Notes 43
2 Modelling with the Dual Problem 47
2.1 Generalized finite sequences 47
2.2 The dual problem 49
2.3 Calculating the Chebyshev point to set distance 52
2.4 Measuring the efficiency of an industrial process 54
2.5 A generalized location problem 55
2.6 Robustness in Bayesian statistics 56
Exercises 59
Notes 61
Part II: Linear Semi infinite Systems 65
3 Alternative Theorems 67
3.1 Linear inequality systems in pattern recognition 67
3.2 Farkas and Gale Alternative Theorems 69
v
vi Contents
3.3 Other alternative theorems 72
Exercises 75
Notes 78
4 Consistency 81
4.1 Extended solutions 81
4.2 Consistency tests 85
4.3 Classifying redundant inequalities 89
Exercises 96
Notes 99
5 Geometry 101
5.1 Introduction 101
5.2 On some classes of semi infinite systems 104
5.3 Geometry of the solution set 111
5.4 Equivalent systems 116
Exercises 120
Notes 125
6 Stability 127
6.1 Stability criteria 127
6.2 Stability of consistent systems 128
6.3 Stability of inconsistent systems 135
6.4 Stability of continuous systems 138
6.5 Stability and redundancy 142
Exercises 143
Notes 147
Part III: Theory of Linear Semi infinite Programming 151
7 Optimality 153
7.1 Introduction 153
7.2 Primal optimality conditions 154
7.3 Dimension of the optimal set 158
7.4 Optimality criteria for the dual 160
7.5 Optimality conditions for the convex SIP 162
Exercises 164
Notes 167
8 Duality 169
8.1 Introduction 169
8.2 Duality gap and the optimal value function 170
8.3 Discretizable and reducible problems 172
Contents vii
8.4 Uniform duality 178
8.5 Approximating optimal solutions 183
8.6 Duality theory for convex SIP 188
Exercises 191
Notes 197
9 Extremality and Boundedness 201
9.1 Introduction 201
9.2 On the primal feasible and optimal sets 202
9.3 On the dual feasible and optimal sets 211
Exercises 220
Notes 224
10 Stability and Well Posedness 227
10.1 Introduction 227
10.2 Optimal value function 228
10.3 Hadamard well posedness 231
10.4 Optimal set mapping 235
10.5 Unicity 237
Exercises 241
Notes 247
Part IV: Methods of Linear Semi infinite Programming 251
11 Local Reduction and Discretization Methods 253
11.1 Introduction 253
11.2 The local reduction approach 255
11.3 Grid discretization methods 257
11.4 Cutting plane discretization 261
11.5 The three phase method 270
11.6 A test problem 273
Exercises 2 79
Notes 281
12 Simplex Like and Exchange Methods 285
12.1 Introduction 285
12.2 A purification method for the dual problem 286
12.3 A dual simplex primal exchange method 287
12.4 A purification scheme for the primal problem 294
12.5 A primal simplex dual exchange method 299
Exercises 303
Notes 307
viii Contents
Appendix 309
A.1 Convex sets 309
A.2 Convex functions 313
Notes 319
Symbols and Abbreviations 321
References 325
Index 339
|
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| id | DE-604.BV012003064 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:19:59Z |
| institution | BVB |
| isbn | 0471970409 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008122228 |
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| physical | XII, 343 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
| record_format | marc |
| series | Mathematical methods in practice |
| series2 | Mathematical methods in practice |
| spelling | Goberna, Miguel Á. Verfasser aut Linear semi-infinite optimization Miguel A. Goberna and Marco A. López Chichester [u.a.] Wiley 1998 XII, 343 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical methods in practice 2 Dualité, Principe de (mathématiques) ram Optimisation mathématique ram optimisation linéaire inriac problème dual inriac problème primal inriac programmation linéaire inriac Duality theory (Mathematics) Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Semiinfinite Optimierung (DE-588)4137036-3 s DE-604 López, Marco A. Verfasser aut Mathematical methods in practice 2 (DE-604)BV035419231 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008122228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goberna, Miguel Á. López, Marco A. Linear semi-infinite optimization Mathematical methods in practice Dualité, Principe de (mathématiques) ram Optimisation mathématique ram optimisation linéaire inriac problème dual inriac problème primal inriac programmation linéaire inriac Duality theory (Mathematics) Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4137036-3 (DE-588)4035816-1 |
| title | Linear semi-infinite optimization |
| title_auth | Linear semi-infinite optimization |
| title_exact_search | Linear semi-infinite optimization |
| title_full | Linear semi-infinite optimization Miguel A. Goberna and Marco A. López |
| title_fullStr | Linear semi-infinite optimization Miguel A. Goberna and Marco A. López |
| title_full_unstemmed | Linear semi-infinite optimization Miguel A. Goberna and Marco A. López |
| title_short | Linear semi-infinite optimization |
| title_sort | linear semi infinite optimization |
| topic | Dualité, Principe de (mathématiques) ram Optimisation mathématique ram optimisation linéaire inriac problème dual inriac problème primal inriac programmation linéaire inriac Duality theory (Mathematics) Mathematical optimization Semiinfinite Optimierung (DE-588)4137036-3 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Dualité, Principe de (mathématiques) Optimisation mathématique optimisation linéaire problème dual problème primal programmation linéaire Duality theory (Mathematics) Mathematical optimization Semiinfinite Optimierung Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008122228&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035419231 |
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