Duality in optimization and variational inequalities:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Taylor & Francis
2002
|
| Series: | Optimizatiton theory and applications
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 313 S. graph. Darst. |
| ISBN: | 0415274796 |
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Record in the Search Index
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| adam_text | DUALITY IN OPTIMIZATION AND VARIATIONAL INEQUALITIES CJ.GOH DEPARTMENT
OF MATHEMATICS, AUCKLAND UNIVERSITY AND DEPARTMENT OF MATHEMATICS AND
STATISTICS, UNIVERSITY OF WESTERN AUSTRALIA AND X.Q. YANG DEPARTMENT OF
APPLIED MATHEMATICS, THE HONG KONG POLYTECHNIC UNIVERSITY IM LONDON AND
NEW YORK CONTENTS FIGURE CAPTIONS XI PREFACE XIII CHAPTER 1 MATHEMATICAL
PRELIMIMARIES 1 1.1 BASIC NOTATIONS AND A LIST OF SYMBOLS 2 1.2 ELEMENTS
OF CONVEX ANALYSIS 5 1.3 FENCHEL TRANSFORM AND CONJUGATE DUALITY 19 1.4
ELEMENTS OF GRAPH THEORY 24 1.5 ELEMENTS OF OPTIMIZATION AND VARIATIONAL
INEQUALITIES 28 1.6 WEAK/STRONG DUALITY, DUALITY GAP AND GAP FUNCTION 34
1.7 MOTIVATIONS FOR STUDYING DUALITY 37 CHAPTER 2 DUALITY IN NETWORK
OPTIMIZATION 41 2.1 DUALITY OF PATHS AND CUTS AND MINIMUM SPANNING TREES
42 2.2 DUALITY IN A PAINTED NETWORK 46 2.3 FLOW, DIVERGENCE, POTENTIAL
AND DIFFERENTIAL 48 2.4 DUALITY OF MAX FLOW MIN CUT 52 2.5 DUALITY OF
MAX MATCH MIN BLOCK 57 VII 2.6 DUALITY OF MAX TENSION MIN PATH 62 2.7
DUALITY OF FEASIBLE FLOW AND FEASIBLE POTENTIAL 66 2.8 DUALITY OF LINEAR
OPTIMAL FLOW AND OPTIMAL POTENTIAL 71 2.9 DUALITY OF CONVEX OPTIMAL FLOW
AND OPTIMAL POTENTIAL 83 CHAPTER 3 DUALITY IN LINEAR SYSTEMS 93 3.1 A
CRASH COURSE IN LINEAR PROGRAMMING 93 3.2 DUALITY IN LINEAR PROGRAMMING
100 3.3 DUALITY AND COMPLEMENTARY SLACKNESS 106 3.4 DUALITY AND THEOREMS
OF ALTERNATIVES 109 3.5 PAINTED INDEX THEORY 114 3.6 DUALITY IN
MONOTROPIC OPTIMIZATION 123 CHAPTER 4 DUALITY IN CONVEX NONLINEAR
SYSTEMS 127 4.1 CONJUGATE DUALITY IN UNCONSTRAINED OPTIMIZATION 128 4.2
OPTIMALITY CONDITIONS FOR CONSTRAINED OPTIMIZATION 131 4.3 LAGRANGIAN
DUALITY 134 4.4 LAGRANGIAN DUALITY SPECIALIZED TO LP, QP AND MP 142 4.5
WOLFE DUALITY AND GAP FUNCTIONS FOR CONVEX OPTIMIZATION 145 CHAPTER 5
DUALITY IN NONCONVEX SYSTEMS 151 5.1 EXAMPLES OF NONZERO DUALITY GAPS
151 5.2 ZERO DUALITY GAP VIA A NONLINEAR LAGRANGIAN FUNCTION 156 5.3
OPTIMALITY CONDITIONS VIA A MONOTONE FUNCTION 159 5.4 OPTIMALITY
CONDITIONS VIA A MONOTONE COMPOSITION FORMULATION 164 5.5 ZERO DUALITY
GAP VIA AN ALTERNATE LAGRANGIAN FUNCTION 174 5.6 ZERO DUALITY GAP FOR A
DISCRETE OPTIMIZATION PROBLEM 178 5.7 ZERO DUALITY GAP VIA AN EXTENDED
LAGRANGIAN FUNCTION 183 VIII CHAPTER 6 DUALITY IN VARIATIONAL
INEQUALITIES 193 6.1 DUALITY IN VARIATIONAL INEQUALITIES 194 6.2 GAP
FUNCTIONS FOR VARIATIONAL INEQUALITIES 199 6.3 PRIMAL AND DUAL GAP
FUNCTIONS FOR EXTENDED VARIATIONAL INEQUALITIES 204 6.4 GAP FUNCTIONS
AND DUAL FENCHEL OPTIMIZATION 208 CHAPTER 7 ELEMENTS OF MULTICRITERIA
OPTIMIZATION 215 7.1 ELEMENTS OF MULTICRITERIA CONVEX ANALYSIS 216 7.2
VECTOR CONJUGATE DUALITY 221 7.3 SCALARIZATION OF MULTICRITERIA
OPTIMIZATION 225 7.4 OPTIMALITY CONDITIONS FOR MULTICRITERIA
OPTIMIZATION 232 CHAPTER 8 DUALITY IN MULTICRITERIA OPTIMIZATION 237 8.1
DUALITY IN LINEAR MULTICRITERIA OPTIMIZATION 238 8.2 CONJUGATE DUALITY
IN CONVEX MULTICRITERIA OPTIMIZATION 243 8.3 LAGRANGIAN DUALITY IN
CONVEX MULTICRITERIA OPTIMIZATION 249 8.4 A CASE OF SYMMETRIE AND SEIF
DUALITY 252 8.5 GAP FUNCTIONS FOR CONVEX MULTICRITERIA OPTIMIZATION 257
8.6 DUALITY IN CONVEX COMPOSITE MULTICRITERIA OPTIMIZATION 262 CHAPTER 9
DUAUETY IN VECTOR VARIATIONAL INEQUALITIES 267 9.1 INTRODUCTION TO VECTOR
VARIATIONAL INEQUALITIES 268 9.2 SCALARIZATION OF VECTOR VARIATIONAL
INEQUALITIES 272 9.3 DUALITY IN EXTENDED VECTOR VARIATIONAL INEQUALITIES
276 9.4 GAP FUNCTIONS FOR EXTENDED VECTOR VARIATIONAL INEQUALITIES 282
9.5 GENERALIZED GAP FUNCTIONS 285 9.6 A SOLUTION METHOD AND A RELATED
GAP FUNCTION 288 REFERENCES 293 INDEX 303 IX
|
| any_adam_object | 1 |
| author | Goh, C. J. Yang, Xiaoqi |
| author_facet | Goh, C. J. Yang, Xiaoqi |
| author_role | aut aut |
| author_sort | Goh, C. J. |
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| dewey-full | 515.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 515.782 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 0415274796 |
| language | English |
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| physical | XVI, 313 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Taylor & Francis |
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| series | Optimizatiton theory and applications |
| series2 | Optimizatiton theory and applications |
| spelling | Goh, C. J. Verfasser aut Duality in optimization and variational inequalities C. J. Goh ; X. Q. Yang London [u.a.] Taylor & Francis 2002 XVI, 313 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Optimizatiton theory and applications 2 Optimierung (DE-588)4043664-0 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf Dualität (DE-588)4013161-0 s Optimierung (DE-588)4043664-0 s Variationsungleichung (DE-588)4187420-1 s DE-604 Yang, Xiaoqi Verfasser aut Optimizatiton theory and applications 2 (DE-604)BV035420075 2 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478727&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goh, C. J. Yang, Xiaoqi Duality in optimization and variational inequalities Optimizatiton theory and applications Optimierung (DE-588)4043664-0 gnd Dualität (DE-588)4013161-0 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4013161-0 (DE-588)4187420-1 |
| title | Duality in optimization and variational inequalities |
| title_auth | Duality in optimization and variational inequalities |
| title_exact_search | Duality in optimization and variational inequalities |
| title_full | Duality in optimization and variational inequalities C. J. Goh ; X. Q. Yang |
| title_fullStr | Duality in optimization and variational inequalities C. J. Goh ; X. Q. Yang |
| title_full_unstemmed | Duality in optimization and variational inequalities C. J. Goh ; X. Q. Yang |
| title_short | Duality in optimization and variational inequalities |
| title_sort | duality in optimization and variational inequalities |
| topic | Optimierung (DE-588)4043664-0 gnd Dualität (DE-588)4013161-0 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Optimierung Dualität Variationsungleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478727&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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