Variational methods in partially ordered spaces:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
2003
|
| Series: | CMS books in mathematics
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 3125 - 344 |
| Physical Description: | XI, 350 Seiten graph. Darst. |
| ISBN: | 0387004521 |
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| 245 | 1 | 0 | |a Variational methods in partially ordered spaces |c Alfred Göpfert ... |
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Record in the Search Index
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|---|---|
| adam_text | ALFRED GOPFERT CHRISTIANE TAMMER HASSAN RIAHI CONSTANTIN ZALINESCU
VARIATIONAL METHODS IN PARTIALLY ORDERED SPACES WITH 13 ILLUSTRATIONS
SPRINGER CONTENTS PREFACE V LIST OF FIGURES XIII 1 EXAMPLES 1 1.1 CONES
IN VECTOR SPACES 1 1.2 EQUILIBRIUM PROBLEMS 3 1.3 LOCATION PROBLEMS IN
TOWN PLANNING 6 1.4 MULTICRITERIA CONTROL PROBLEMS 8 1.5 MULTICRITERIA
FRACTIONAL PROGRAMMING PROBLEMS 10 1.6 STOCHASTIC EFFICIENCY IN A SET 11
2 FUNCTIONAL ANALYSIS OVER CONES 13 2.1 ORDER STRUCTURES 13 2.2
FUNCTIONAL ANALYSIS AND CONVEXITY 26 2.3 SEPARATION THEOREMS FOR NOT
NECESSARILY CONVEX SETS 39 2.4 CONVEXITY NOTIONS FOR SETS AND
MULTIFUNCTIONS 45 2.5 CONTINUITY NOTIONS FOR MULTIFUNCTIONS 51 2.6
CONTINUITY PROPERTIES OF MULTIFUNCTIONS UNDER CONVEXITY ASSUMPTIONS 70
2.7 TANGENT CONES AND DIFFERENTIABILITY OF MULTIFUNCTIONS 73 3
OPTIMIZATION IN PARTIALLY ORDERED SPACES 81 3.1 SOLUTION CONCEPTS 81
3.1.1 APPROXIMATE MINIMALITY 81 3.1.2 A GENERAL SCALARIZATION METHOD 84
3.2 EXISTENCE RESULTS FOR EFFICIENT POINTS 86 3.2.1 PRELIMINARY NOTIONS
AND RESULTS CONCERNING TRANSITIVE RELATIONS 87 3.2.2 EXISTENCE OF
MAXIMAL ELEMENTS WITH RESPECT TO TRANSITIVE RELATIONS 89 CONTENTS 3.2.3
EXISTENCE OF EFFICIENT POINTS WITH RESPECT TO CONES .... 94 3.2.4 TYPES
OF CONVEX CONES AND COMPACTNESS WITH RESPECT TO CONES 101 3.2.5
CLASSIFICATION OF EXISTENCE RESULTS FOR EFFICIENT POINTS . . 104 3.2.6
SOME DENSITY AND CONNECTEDNESS RESULTS 110 3.3 CONTINUITY PROPERTIES
WITH RESPECT TO A SCALARIZATION PARAMETER 115 3.4 WELL-POSEDNESS OF
VECTOR OPTIMIZATION PROBLEMS 119 3.5 CONTINUITY PROPERTIES 122 3.5.1
CONTINUITY PROPERTIES OF OPTIMAL-VALUE MULTIFUNCTIONS . 122 3.5.2
CONTINUITY PROPERTIES FOR THE OPTIMAL MULTIFUNCTION IN THE CASE OF
MOVING CONES 135 3.5.3 CONTINUITY PROPERTIES FOR THE SOLUTION
MULTIFUNCTION . .. 138 3.6 SENSITIVITY OF VECTOR OPTIMIZATION PROBLEMS
141 3.7 DUALITY 154 3.7.1 DUALITY WITHOUT SCALARIZATION 155 3.7.2
DUALITY BY SCALARIZATION 159 3.7.3 DUALITY FOR APPROXIMATION PROBLEMS
162 3.8 VECTOR EQUILIBRIUM PROBLEMS AND RELATED TOPICS 168 3.8.1 VECTOR
EQUILIBRIUM PROBLEMS 169 3.8.2 GENERAL VECTOR MONOTONICITY 171 3.8.3
EXISTENCE OF VECTOR EQUILIBRIA BY USE OF THE GENERALIZED KKM LEMMA 172
3.8.4 EXISTENCE BY SCALARIZATION OF VECTOR EQUILIBRIUM PROBLEMS 174
3.8.5 SOME KNOWLEDGE ABOUT THE ASSUMPTIONS 177 3.8.6 SOME PARTICULAR
CASES 180 3.8.7 MIXED VECTOR EQUILIBRIUM PROBLEMS 183 3.9 APPLICATIONS
TO VECTOR VARIATIONAL INEQUALITIES 186 3.9.1 VECTOR VARIATIONAL-LIKE
INEQUALITIES 186 3.9.2 PERTURBED VECTOR VARIATIONAL INEQUALITIES 188
3.9.3 HEMIVARIATIONAL INEQUALITY SYSTEMS 189 3.9.4 VECTOR
COMPLEMENTARITY PROBLEMS 192 3.9.5 APPLICATION TO VECTOR OPTIMIZATION
PROBLEMS 194 3.9.6 MINIMAX THEOREM FOR VECTOR-VALUED MAPPINGS 196 3.10
MINIMAL-POINT THEOREMS IN PRODUCT SPACES AND CORRESPONDING VARIATIONAL
PRINCIPLES 197 3.10.1 NOT AUTHENTIC MINIMAL-POINT THEOREMS 199 3.10.2
AUTHENTIC MINIMAL-POINT THEOREMS 202 3.10.3 MINIMAL-POINT THEOREMS AND
GAUGE TECHNIQUES 205 3.10.4 MINIMAL-POINT THEOREMS AND CONE-VALUED
METRICS .... 209 3.10.5 FIXED POINT THEOREMS OF KIRK-CARISTI TYPE 212
3.11 OPTIMALITY CONDITIONS 213 3.11.1 LAGRANGE MULTIPLIERS AND SADDLE
POINT ASSERTIONS 213 3.11.2 E-SADDLE POINT ASSERTIONS 218 CONTENTS XI 4
APPLICATIONS 229 4.1 APPROXIMATION PROBLEMS 229 4.1.1 GENERAL
APPROXIMATION PROBLEMS 229 4.1.2 FINITE-DIMENSIONAL APPROXIMATION
PROBLEMS 235 4.1.3 LP-APPROXIMATION PROBLEMS 241 4.1.4 EXAMPLE: THE
INVERSE STEFAN PROBLEM 242 4.2 SOLUTION PROCEDURES 244 4.2.1 A
PROXIMAL-POINT ALGORITHM FOR REAL-VALUED CONTROL APPROXIMATION PROBLEMS
244 4.2.2 COMPUTER PROGRAMS FOR THE APPLICATION OF THE PROXIMAL-POINT
ALGORITHM 259 4.2.3 AN INTERACTIVE ALGORITHM FOR THE VECTOR CONTROL
APPROXIMATION PROBLEM 263 4.2.4 PROXIMAL ALGORITHMS FOR VECTOR
EQUILIBRIUM PROBLEMS . 266 4.2.5 RELAXATION AND PENALIZATION 277 4.3
LOCATION PROBLEMS 282 4.3.1 FORMULATION OF THE PROBLEM 282 4.3.2 AN
ALGORITHM FOR THE MULTICRITERIA LOCATION PROBLEM . . 285 4.3.3 A
MATHEMATICA PROGRAM FOR SOLVING THE MULTICRITERIA LOCATION PROBLEM 286
4.3.4 COMPARISON OF ALTERNATIVES 287 4.3.5 APPLICATION TO A PROBLEM OF
TOWN PLANNING 289 4.4 MULTICRITERIA FRACTIONAL PROGRAMMING 294 4.4.1
SOLUTION CONCEPTS 294 4.4.2 GENERALIZED DINKELBACH TRANSFORMATION 297
4.4.3 POSSIBILITIES FOR A SOLUTION APPROACH 300 4.5 MULTICRITERIA
CONTROL PROBLEMS 303 4.5.1 THE FORMULATION OF THE PROBLEM 303 4.5.2 AN
E-MINIMUM PRINCIPLE FOR MULTICRITERIA OPTIMAL CONTROL PROBLEMS 304 4.5.3
A MULTICRITERIA STOCHASTIC CONTROL PROBLEM 309 4.6 STOCHASTIC EFFICIENCY
IN A SET 316 LIST OF ABBREVIATIONS 319 REFERENCES 325 INDEX 345
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| indexdate | 2024-07-09T19:12:21Z |
| institution | BVB |
| isbn | 0387004521 |
| language | English |
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| physical | XI, 350 Seiten graph. Darst. |
| publishDate | 2003 |
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| series | CMS books in mathematics |
| series2 | CMS books in mathematics |
| spelling | Variational methods in partially ordered spaces Alfred Göpfert ... New York [u.a.] Springer 2003 XI, 350 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics 17 Literaturverz. S. 3125 - 344 Espaces partiellement ordonnés Espaces vectoriels Optimisation mathématique Partiële orde gtt Variatierekening gtt Mathematical optimization Partially ordered spaces Vector spaces Mehrkriterielle Optimierung (DE-588)4610682-0 gnd rswk-swf Mehrkriterielle Optimierung (DE-588)4610682-0 s DE-604 Göpfert, Alfred 1934-2023 Sonstige (DE-588)137247575 oth CMS books in mathematics 17 (DE-604)BV013248581 17 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Variational methods in partially ordered spaces CMS books in mathematics Espaces partiellement ordonnés Espaces vectoriels Optimisation mathématique Partiële orde gtt Variatierekening gtt Mathematical optimization Partially ordered spaces Vector spaces Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| subject_GND | (DE-588)4610682-0 |
| title | Variational methods in partially ordered spaces |
| title_auth | Variational methods in partially ordered spaces |
| title_exact_search | Variational methods in partially ordered spaces |
| title_full | Variational methods in partially ordered spaces Alfred Göpfert ... |
| title_fullStr | Variational methods in partially ordered spaces Alfred Göpfert ... |
| title_full_unstemmed | Variational methods in partially ordered spaces Alfred Göpfert ... |
| title_short | Variational methods in partially ordered spaces |
| title_sort | variational methods in partially ordered spaces |
| topic | Espaces partiellement ordonnés Espaces vectoriels Optimisation mathématique Partiële orde gtt Variatierekening gtt Mathematical optimization Partially ordered spaces Vector spaces Mehrkriterielle Optimierung (DE-588)4610682-0 gnd |
| topic_facet | Espaces partiellement ordonnés Espaces vectoriels Optimisation mathématique Partiële orde Variatierekening Mathematical optimization Partially ordered spaces Vector spaces Mehrkriterielle Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010250143&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013248581 |
| work_keys_str_mv | AT gopfertalfred variationalmethodsinpartiallyorderedspaces |