Equilibrium problems and variational models:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Kluwer
2003
|
| Schriftenreihe: | Nonconvex optimization and its applications
68 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XII, 445 S. graph. Darst. |
| ISBN: | 1402074700 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804136137686515713 |
|---|---|
| adam_text | EQUILIBRIUM PROBLEMS AND VARIATIONAL MODELS EDITED BY PATRIZIA DANIELE
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CATANIA 95125 CATANIA ITALY
FRANCO GIANNESSI DEPARTMENT OF MATHEMATICS UNIVERSITY OF PISA 56127 PISA
ITALY ANTONINO MAUGERI DEPARTMENT OF MATHEMATICS UNIVERSITY OF CATANIA
95125 CATANIA ITALY CONTENTS PREFACE XIII ON VECTOR QUASI-EQUILIBRIUM
PROBLEMS 1 QAMRUL HASAN ANSARI AND JEN-CHIH YAO 1. INTRODUCTION 1 2.
PRELIMINARIES 3 3. EXISTENCE RESULTS 6 4. SOME APPLICATIONS 10
REFERENCES 15 THE LOG-QUADRATIC PROXIMAL METHODOLOGY IN CONVEX OP-
TIMIZATION ALGORITHMS AND VARIATIONAL INEQUALITIES 19 ALFRED AUSLENDER
AND MARC TEBOULLE 1. INTRODUCTION 20 2. LAGRANGIANS AND PROXIMAL METHODS
21 2.1. THE QUADRATIC AUGMENTED LAGRANGIAN 21 2.2. PROXIMAL MINIMIZATION
ALGORITHMS 22 2.3. ENTROPIE PROXIMAL METHODS AND MODIFIED LAGRANGIANS 24
2.4. DIFFICULTIES WITH ENTROPIE PROXIMAL METHODS 26 2.5. TOWARD
SOLUTIONS TO DIFFICULTIES 28 3. THE LOGARITHMIC-QUADRATIC PROXIMAL
FRAMEWORK 29 3.1. THE LQ-FUNCTION AND ITS CONJUGATE: BASIC PROPERTIES 29
3.2. THE LOGARITHMIC-QUADRATIC PROXIMAL MINIMIZATION 31 4. THE LQP IN
ACTION 33 4.1. PRIMAL LQP FOR VARIATIONAL INEQUALITIES OVER POLYHEDRA 33
4.2. LAGRANGIAN METHODS FOR CONVEX OPTIMIZATION AND VARIATIONAL
INEQUALITIES 34 4.3. DUAL AND PRIMAL-DUAL DECOMPOSITION SCHEMES 35 4.4.
PRIMAL DECOMPOSITION: BLOCK GAUSS-SEIDEL SCHEMES FOR LINEARLY
CONSTRAINED PROBLEMS 39 VI 4.5. CONVEX FEASIBILITY PROBLEMS 41 4.6.
BUENDLE METHODS IN NONSMOOTH OPTIMIZATION 43 REFERENCES 45 THE CONTINUUM
MODEL OF TRANSPORTATION PROBLEM 53 PATRIZIA DANIELE, GIOVANNA IDONE AND
ANTONINO MAUGERI 1. INTRODUCTION 53 2. CALCULUS OF THE SOLUTION 56
REFERENCES 59 THE ECONOMIC MODEL FOR DEMAND-SUPPLY PROBLEMS 61 PATRIZIA
DANIELE AND ANTONINO MAUGERI 1. INTRODUCTION 61 2. THE FIRST PHASE:
FORMALIZATION OF THE EQUILIBRIUM 62 3. THE SECOND PHASE: FORMALIZATION
OF THE EQUILIBRIUM 67 4. THE DEPENDENCE OF THE SECOND PHASE ON THE FIRST
ONE 70 5. GENERAL MODEL 71 6. EXAMPLE 72 REFERENCES 77 CONSTRAINED
PROBLEMS OF CALCULUS OF VARIATIONS VIA PENAL- IZATION TECHNIQUE 79
VLADIMIR F. DEMYANOV 1. INTRODUCTION 79 2. STATEMENT OF THE PROBLEM 80
3. AN EQUIVALENT STATEMENT OF THE PROBLEM 81 4. LOCAL MINIMA 83 5.
PENALTY FUNCTIONS 86 6. EXACT PENALTY FUNCTIONS 88 6.1. PROPERTIES OF
THE FUNCTION 88 6.2. PROPERTIES OF THE FUNCTION G 94 6.3. THE RATE OF
DESCENT OF THE FUNCTION
6.4. AN EXACT PENALTY FUNCTION 99 7. NECESSARY CONDITIONS FOR AN
EXTREMUM 100 7.1. NECESSARY CONDITIONS GENERATED BY CLASSICAL VARIATIONS
100 7.2. DISCUSSION AND REMARKS 103 REFERENCES 106 VI] VARIATIONAL
PROBLEMS WITH CONSTRAINTS INVOLVING HIGHER- ORDER DERIVATIVES 109
VLADIMIR F. DEMYANOV AND FRANCO GIANNESSI 1. INTRODUCTION 109 2.
STATEMENT OF THE PROBLEM 110 3. AN EQUIVALENT STATEMENT OF THE PROBLEM
111 4. LOCAL MINIMA 114 5. PROPERTIES OF THE FUNCTION 115 5.1. A
CLASSICAL VARIATION OF Z 115 5.2. THE CASE Z & Z 117 5.3. THE CASE Z * Z
120 6. EXACT PENALTY FUNCTIONS 123 6.1. PROPERTIES OF THE FUNCTION G 123
6.2. AN EXACT PENALTY FUNCTION 127 7. NECESSARY CONDITIONS FOR AN
EXTREMUM 127 REFERENCES 133 ON THE STRONG SOLVABILITY OF A UNILATERAL
BOUNDARY VALUE PROBLEM FOR NONLINEAR PARABOLIC OPERATORS IN THE PLANE
135 ROSALBA DI VINCENZO 1. INTRODUCTION 135 2. HYPOTHESES AND RESULTS
136 3. PRELIMINARY RESULTS 137 4. PROOF OF THE THEOREMS 138 REFERENCES
140 SOLVING A SPECIAL CLASS OF DISCRETE OPTIMAL CONTROL PROB- LEMS VIA A
PARALLEL INTERIOR-POINT METHOD 141 CARLA DURAZZI, VALERIA RUGGIERO AND
GAETANO ZANGHIRATI 1. INTRODUCTION 142 2. EYAMEWORK OF THE METHOD 143 3.
GLOBAL CONVERGENCE 149 4. A SPECIAL CLASS OF DISCRETE OPTIMAL CONTROL
PROBLEMS 152 5. NUMERICAL EXPERIMENTS 157 6. CONCLUSIONS 160 REFERENCES
160 VLLL SOLVING LARGE SCALE FIXED CHARGE NETWORK FLOW PROBLEMS 163
BURAK EK§IOGLU, SANDRA DUNI EK§IOGLU AND PANOS M. PARDALOS 1.
INTRODUCTION 164 2. PROBLEM DEFINITION AND FORMULATION 166 3. SOLUTION
PROCEDURA 167 3.1. THEDSSP 167 3.2. LOCAL SEARCH 169 4. COMPUTATIONAL
RESULTS 171 5. CONCLUDING REMARKS 181 REFERENCES 181 VARIABLE PROJECTION
METHODS FOR LARGE-SCALE QUADRATIC OPTIMIZATION IN DATA ANALYSIS
APPLICATIONS 185 EMANUELE GALLIGANI, VALERIA RUGGIERO AND LUCA ZANNI 1.
INTRODUCTION 185 2. LARGE QP PROBLEMS IN TRAINING SUPPORT VECTOR
MACHINES 188 3. NUMERICAL SOLUTION OF IMAGE RESTORATION PROBLEM 193 4. A
BIVARIATE INTERPOLATION PROBLEM 200 5. CONCLUSIONS 206 REFERENCES 207
STRONG SOLVABILITY OF BOUNDARY VALUE PROBLEMS IN ELASTICITY WITH
UNILATERAL CONSTRAINTS 213 SOFIA GIUFFRE 1. INTRODUCTION 213 2. BASIC
ASSUMPTIONS AND MAIN RESULTS 215 3. PRELIMINARY RESULTS 217 4. PROOF OF
THE THEOREMS 218 REFERENCES 223 TIME DEPENDENT VARIATIONAL INEQUALITIES
- SOME RECENT TRENDS 225 JOACHIM GWINNER 1. INTRODUCTION 226 2. TIME -
AN ADDITIONAL PARAMETER IN VARIATIONAL INEQUALITIES 229 IX 2.1.
TIME-DEPENDENT VARIATIONAL INEQUALITIES AND QUASI-VARIATIONAL IN-
EQUALITIES 230 2.2. SOME CLASSIC RESULTS ON THE DIFFERENTIABILITY OF THE
PROJECTION ON CLOSED CONVEX SUBSETS IN HUBERT SPACE 236 2.3.
TIME-DEPENDENT VARIATIONAL INEQUALITIES WITH MEMORY TERMS 237 3.
ORDINARY DIFFERENTIAL INCLUSIONS WITH CONVEX CONSTRAINTS: SWEEPING
PROCESSES 240 3.1. MOVING CONVEX SETS AND SYSTEMS WITH HYSTERESIS 241
3.2. SWEEPING PROCESSES AND GENERALIZATIONS 242 4. PROJECTED DYNAMICAL
SYSTEMS 247 4.1. DIFFERENTIABILITY OF THE PROJECTION ONTO CLOSED CONVEX
SUBSETS REVISITED 247 4.2. PROJECTED DYNAMICAL SYSTEMS AND STATIONARITY
250 4.3. WELL-POSEDNESS FOR PROJECTED DYNAMICAL SYSTEMS 251 5. SOME
ASYMPTOTIC RESULTS 252 5.1. SOME CLASSICAL RESULTS 252 5.2. AN
ASYMPTOTIC RESULT FOR FUELL DISCRETIZATION 253 5.3. SOME CONVERGENCE
RESULTS FOR CONTINUOUS-TIME SUBGRADIENT PROCE- DURES FOR CONVEX
OPTIMIZATION 256 REFERENCES 259 ON THE CONTRACTIBILITY OF THE EFFLCIENT
AND WEAKLY EFFICIENT SETS IN R 2 265 NGUYEN QUANG HUY, TA DUY PHUONG AND
NGUYEN DONG YEN 1. INTRODUCTION 265 2. PRELIMINARIES 266 3. TOPOLOGICAL
STRUCTURE OF THE EFFICIENT SETS OF COMPACT CONVEX SETS 267 4. EXAMPLE
276 REFERENCES 278 EXISTENCE THEOREMS FOR A CLASS OF VARIATIONAL
INEQUALITIES AND APPLICATIONS TO A CONTINUOUS MODEL OF TRANSPORTATION
281 FRANCESCO MARINO 1. INTRODUCTION 281 2. CONTINUOUS TRANSPORTATION
MODEL 282 3. EXISTENCE THEOREM 284 REFERENCES 287 X ON AUXILIARY
PRINCIPLE FOR EQUILIBRIUM PROBLEMS 289 GIANDOMENICO MASTROENI 1.
INTRODUCTION 289 2. THE AUXILIARY EQUILIBRIUM PROBLEM 291 3. THE
AUXILIARY PROBLEM PRINCIPLE 293 4. APPLICATIONS TO VARIATIONAL
INEQUALITIES AND OPTIMIZATION PROBLEMS 295 5. CONCLUDING REMARKS 297
REFERENCES 297 MULTICRITERIA SPATIAL PRICE NETWORKS: STATICS AND DYNAM-
ICS 299 ANNA NAGURNEY, JUNE DONG AND DING ZHANG 1. INTRODUCTION 299 2.
THE MULTICRITERIA SPATIAL PRICE MODEL 301 3. QUALITATIVE PROPERTIES 306
4. THE DYNAMICS 309 5. THE DISCRETE-TIME ALGORITHM 311 6. NUMERICAL
EXAMPLES 314 7. SUMMARY AND CONCLUSIONS 318 REFERENCES 319 NON REGULAER
DATA IN UNILATERAL VARIATIONAL PROBLEMS 323 PIRRO OPPEZZI 1.
INTRODUCTION 323 2. THE APPROACH BY TRUNCATION AND APPROXIMATION 324 3.
RENORMALIZED FORMULATION 328 4. MULTIVALUED OPERATORS AND MORE GENERAL
MEASURES 328 5. UNIQUENESS AND CONVERGENCE 330 REFERENCES 331
EQUILIBRIUM CONCEPTS IN TRANSPORTATION NETWORKS: GENERALIZED WARDROP
CONDITIONS AND VARIATIONAL FOR- MULATIONS 333 MASSIMO PAPPALARDO AND
MAURO PASSACANTANDO 1. INTRODUCTION 2. EQUILIBRIUM MODEL IN A TRAFFIC
NETWORK 333 334 XI REFERENCES 344 VARIATIONAL GEOMETRY AND EQUILIBRIUM
347 MICHAEL PATRIKSSON AND R. TYRRELL ROCKAFELLAR 1. INTRODUCTION 347 2.
VARIATIONAL INEQUALITIES AND NORMALS TO CONVEX SETS 349 3.
QUASI-VARIATIONAL INEQUALITIES AND NORMALS TO GENERAL SETS 352 4.
CALCULUS AND SOLUTION PERTURBATIONS 357 5. APPLICATION TO AN EQUILIBRIUM
MODEL WITH AGGREGATION 361 REFERENCES 367 ON THE CALCULATION OF
EQUILIBRIUM IN TIME DEPENDENT TRAFFIC NETWORKS 369 FABIO RACITI 1.
INTRODUCTION 369 2. CALCULATION OF EQUILIBRIA 370 3. THE ALGORITHM 371
4. APPLICATIONS AND EXAMPLES 372 5. CONCLUSIONS 376 REFERENCES 376
MECHANICAL EQUILIBRIUM AND EQUILIBRIUM SYSTEMS 379 TAMDS RAPCSDK 1.
INTRODUCTION 379 2. PHYSICAL MOTIVATION 380 3. STATEMENT OF THE
MECHANICAL FORCE EQUILIBRIUM PROBLEM 381 4. THE PRINCIPLE OF VIRTUAL
WORK 382 5. CHARACTERIZATION OF THE CONSTRAINTS 383 6. QUASI-VARIATIONAL
INEQUALITIES (QVI) 384 7. PRINCIPLE OF VIRTUAL WORK IN FORCE FIELDS
UNDER SCLERONOMIC AND HOLO- NOMIC CONSTRAINTS 385 8. DUAL FORM OF THE
PRINCIPLE OF VIRTUAL WORK IN FORCE FIELD UNDER SCLERO- NOMIC AND
HOLONOMIC CONSTRAINTS 388 9. PROCEDURE FOR SOLVING MECHANICAL
EQUILIBRIUM PROBLEMS 391 10. EXISTENCE OF SOLUTIONS 395 REFERENCES 397
XLL FALSE NUMERICAL CONVERGENCE IN SOME GENERALIZED NEWTON METHODS 401
STEPHEN M. ROBINSON 1. INTRODUCTION 401 2. SOME GENERALIZED NEWTON
METHODS 402 3. FALSE NUMERICAL CONVERGENCE 405 4. AN EXAMPLE 408 5.
AVOIDING FALSE NUMERICAL CONVERGENCE 411 REFERENCES 415 DISTANCE TO THE
SOLUTION SET OF AN INEQUALITY WITH AN INCREASING FUNCTION 417 ALEX M.
RUBINOV 1. INTRODUCTION 417 2. PRELIMINARIES 418 3. DISTANCE TO THE
SOLUTION SET OF THE INEQUALITY WITH AN ARBITRARY INCREAS- ING FUNCTION
420 4. DISTANCE TO THE SOLUTION SET OF THE INEQUALITY WITH AN ICAR
FUNCTION 423 5. INEQUALITIES WITH AN INCREASING FUNCTION DEFINED ON THE
ENTIRE SPACE 427 6. INEQUALITIES WITH A TOPICAL FUNCTION 429 REFERENCES
430 TRANSPORTATION NETWORKS WITH CAPACITY CONSTRAINTS 433 LAURA SCRIMALI
1. INTRODUCTION 433 2. WARDROP S GENERALIZED EQUILIBRIUM CONDITION 434
3. A TRIANGULAER NETWORK 436 4. MORE ABOUT GENERALIZED EQUILIBRIUM
PRINCIPLE 438 5. CAPACITY CONSTRAINTS AND PARADOX 442 REFERENCES 443
|
| adam_txt |
EQUILIBRIUM PROBLEMS AND VARIATIONAL MODELS EDITED BY PATRIZIA DANIELE
DEPARTMENT OF MATHEMATICS UNIVERSITY OF CATANIA 95125 CATANIA ITALY
FRANCO GIANNESSI DEPARTMENT OF MATHEMATICS UNIVERSITY OF PISA 56127 PISA
ITALY ANTONINO MAUGERI DEPARTMENT OF MATHEMATICS UNIVERSITY OF CATANIA
95125 CATANIA ITALY CONTENTS PREFACE XIII ON VECTOR QUASI-EQUILIBRIUM
PROBLEMS 1 QAMRUL HASAN ANSARI AND JEN-CHIH YAO 1. INTRODUCTION 1 2.
PRELIMINARIES 3 3. EXISTENCE RESULTS 6 4. SOME APPLICATIONS 10
REFERENCES 15 THE LOG-QUADRATIC PROXIMAL METHODOLOGY IN CONVEX OP-
TIMIZATION ALGORITHMS AND VARIATIONAL INEQUALITIES 19 ALFRED AUSLENDER
AND MARC TEBOULLE 1. INTRODUCTION 20 2. LAGRANGIANS AND PROXIMAL METHODS
21 2.1. THE QUADRATIC AUGMENTED LAGRANGIAN 21 2.2. PROXIMAL MINIMIZATION
ALGORITHMS 22 2.3. ENTROPIE PROXIMAL METHODS AND MODIFIED LAGRANGIANS 24
2.4. DIFFICULTIES WITH ENTROPIE PROXIMAL METHODS 26 2.5. TOWARD
SOLUTIONS TO DIFFICULTIES 28 3. THE LOGARITHMIC-QUADRATIC PROXIMAL
FRAMEWORK 29 3.1. THE LQ-FUNCTION AND ITS CONJUGATE: BASIC PROPERTIES 29
3.2. THE LOGARITHMIC-QUADRATIC PROXIMAL MINIMIZATION 31 4. THE LQP IN
ACTION 33 4.1. PRIMAL LQP FOR VARIATIONAL INEQUALITIES OVER POLYHEDRA 33
4.2. LAGRANGIAN METHODS FOR CONVEX OPTIMIZATION AND VARIATIONAL
INEQUALITIES 34 4.3. DUAL AND PRIMAL-DUAL DECOMPOSITION SCHEMES 35 4.4.
PRIMAL DECOMPOSITION: BLOCK GAUSS-SEIDEL SCHEMES FOR LINEARLY
CONSTRAINED PROBLEMS 39 VI 4.5. CONVEX FEASIBILITY PROBLEMS 41 4.6.
BUENDLE METHODS IN NONSMOOTH OPTIMIZATION 43 REFERENCES 45 THE CONTINUUM
MODEL OF TRANSPORTATION PROBLEM 53 PATRIZIA DANIELE, GIOVANNA IDONE AND
ANTONINO MAUGERI 1. INTRODUCTION 53 2. CALCULUS OF THE SOLUTION 56
REFERENCES 59 THE ECONOMIC MODEL FOR DEMAND-SUPPLY PROBLEMS 61 PATRIZIA
DANIELE AND ANTONINO MAUGERI 1. INTRODUCTION 61 2. THE FIRST PHASE:
FORMALIZATION OF THE EQUILIBRIUM 62 3. THE SECOND PHASE: FORMALIZATION
OF THE EQUILIBRIUM 67 4. THE DEPENDENCE OF THE SECOND PHASE ON THE FIRST
ONE 70 5. GENERAL MODEL 71 6. EXAMPLE 72 REFERENCES 77 CONSTRAINED
PROBLEMS OF CALCULUS OF VARIATIONS VIA PENAL- IZATION TECHNIQUE 79
VLADIMIR F. DEMYANOV 1. INTRODUCTION 79 2. STATEMENT OF THE PROBLEM 80
3. AN EQUIVALENT STATEMENT OF THE PROBLEM 81 4. LOCAL MINIMA 83 5.
PENALTY FUNCTIONS 86 6. EXACT PENALTY FUNCTIONS 88 6.1. PROPERTIES OF
THE FUNCTION 88 6.2. PROPERTIES OF THE FUNCTION G 94 6.3. THE RATE OF
DESCENT OF THE FUNCTION
6.4. AN EXACT PENALTY FUNCTION 99 7. NECESSARY CONDITIONS FOR AN
EXTREMUM 100 7.1. NECESSARY CONDITIONS GENERATED BY CLASSICAL VARIATIONS
100 7.2. DISCUSSION AND REMARKS 103 REFERENCES 106 VI] VARIATIONAL
PROBLEMS WITH CONSTRAINTS INVOLVING HIGHER- ORDER DERIVATIVES 109
VLADIMIR F. DEMYANOV AND FRANCO GIANNESSI 1. INTRODUCTION 109 2.
STATEMENT OF THE PROBLEM 110 3. AN EQUIVALENT STATEMENT OF THE PROBLEM
111 4. LOCAL MINIMA 114 5. PROPERTIES OF THE FUNCTION 115 5.1. A
CLASSICAL VARIATION OF Z 115 5.2. THE CASE Z & Z 117 5.3. THE CASE Z * Z
120 6. EXACT PENALTY FUNCTIONS 123 6.1. PROPERTIES OF THE FUNCTION G 123
6.2. AN EXACT PENALTY FUNCTION 127 7. NECESSARY CONDITIONS FOR AN
EXTREMUM 127 REFERENCES 133 ON THE STRONG SOLVABILITY OF A UNILATERAL
BOUNDARY VALUE PROBLEM FOR NONLINEAR PARABOLIC OPERATORS IN THE PLANE
135 ROSALBA DI VINCENZO 1. INTRODUCTION 135 2. HYPOTHESES AND RESULTS
136 3. PRELIMINARY RESULTS 137 4. PROOF OF THE THEOREMS 138 REFERENCES
140 SOLVING A SPECIAL CLASS OF DISCRETE OPTIMAL CONTROL PROB- LEMS VIA A
PARALLEL INTERIOR-POINT METHOD 141 CARLA DURAZZI, VALERIA RUGGIERO AND
GAETANO ZANGHIRATI 1. INTRODUCTION 142 2. EYAMEWORK OF THE METHOD 143 3.
GLOBAL CONVERGENCE 149 4. A SPECIAL CLASS OF DISCRETE OPTIMAL CONTROL
PROBLEMS 152 5. NUMERICAL EXPERIMENTS 157 6. CONCLUSIONS 160 REFERENCES
160 VLLL SOLVING LARGE SCALE FIXED CHARGE NETWORK FLOW PROBLEMS 163
BURAK EK§IOGLU, SANDRA DUNI EK§IOGLU AND PANOS M. PARDALOS 1.
INTRODUCTION 164 2. PROBLEM DEFINITION AND FORMULATION 166 3. SOLUTION
PROCEDURA 167 3.1. THEDSSP 167 3.2. LOCAL SEARCH 169 4. COMPUTATIONAL
RESULTS 171 5. CONCLUDING REMARKS 181 REFERENCES 181 VARIABLE PROJECTION
METHODS FOR LARGE-SCALE QUADRATIC OPTIMIZATION IN DATA ANALYSIS
APPLICATIONS 185 EMANUELE GALLIGANI, VALERIA RUGGIERO AND LUCA ZANNI 1.
INTRODUCTION 185 2. LARGE QP PROBLEMS IN TRAINING SUPPORT VECTOR
MACHINES 188 3. NUMERICAL SOLUTION OF IMAGE RESTORATION PROBLEM 193 4. A
BIVARIATE INTERPOLATION PROBLEM 200 5. CONCLUSIONS 206 REFERENCES 207
STRONG SOLVABILITY OF BOUNDARY VALUE PROBLEMS IN ELASTICITY WITH
UNILATERAL CONSTRAINTS 213 SOFIA GIUFFRE 1. INTRODUCTION 213 2. BASIC
ASSUMPTIONS AND MAIN RESULTS 215 3. PRELIMINARY RESULTS 217 4. PROOF OF
THE THEOREMS 218 REFERENCES 223 TIME DEPENDENT VARIATIONAL INEQUALITIES
- SOME RECENT TRENDS 225 JOACHIM GWINNER 1. INTRODUCTION 226 2. TIME -
AN ADDITIONAL PARAMETER IN VARIATIONAL INEQUALITIES 229 IX 2.1.
TIME-DEPENDENT VARIATIONAL INEQUALITIES AND QUASI-VARIATIONAL IN-
EQUALITIES 230 2.2. SOME CLASSIC RESULTS ON THE DIFFERENTIABILITY OF THE
PROJECTION ON CLOSED CONVEX SUBSETS IN HUBERT SPACE 236 2.3.
TIME-DEPENDENT VARIATIONAL INEQUALITIES WITH MEMORY TERMS 237 3.
ORDINARY DIFFERENTIAL INCLUSIONS WITH CONVEX CONSTRAINTS: SWEEPING
PROCESSES 240 3.1. MOVING CONVEX SETS AND SYSTEMS WITH HYSTERESIS 241
3.2. SWEEPING PROCESSES AND GENERALIZATIONS 242 4. PROJECTED DYNAMICAL
SYSTEMS 247 4.1. DIFFERENTIABILITY OF THE PROJECTION ONTO CLOSED CONVEX
SUBSETS REVISITED 247 4.2. PROJECTED DYNAMICAL SYSTEMS AND STATIONARITY
250 4.3. WELL-POSEDNESS FOR PROJECTED DYNAMICAL SYSTEMS 251 5. SOME
ASYMPTOTIC RESULTS 252 5.1. SOME CLASSICAL RESULTS 252 5.2. AN
ASYMPTOTIC RESULT FOR FUELL DISCRETIZATION 253 5.3. SOME CONVERGENCE
RESULTS FOR CONTINUOUS-TIME SUBGRADIENT PROCE- DURES FOR CONVEX
OPTIMIZATION 256 REFERENCES 259 ON THE CONTRACTIBILITY OF THE EFFLCIENT
AND WEAKLY EFFICIENT SETS IN R 2 265 NGUYEN QUANG HUY, TA DUY PHUONG AND
NGUYEN DONG YEN 1. INTRODUCTION 265 2. PRELIMINARIES 266 3. TOPOLOGICAL
STRUCTURE OF THE EFFICIENT SETS OF COMPACT CONVEX SETS 267 4. EXAMPLE
276 REFERENCES 278 EXISTENCE THEOREMS FOR A CLASS OF VARIATIONAL
INEQUALITIES AND APPLICATIONS TO A CONTINUOUS MODEL OF TRANSPORTATION
281 FRANCESCO MARINO 1. INTRODUCTION 281 2. CONTINUOUS TRANSPORTATION
MODEL 282 3. EXISTENCE THEOREM 284 REFERENCES 287 X ON AUXILIARY
PRINCIPLE FOR EQUILIBRIUM PROBLEMS 289 GIANDOMENICO MASTROENI 1.
INTRODUCTION 289 2. THE AUXILIARY EQUILIBRIUM PROBLEM 291 3. THE
AUXILIARY PROBLEM PRINCIPLE 293 4. APPLICATIONS TO VARIATIONAL
INEQUALITIES AND OPTIMIZATION PROBLEMS 295 5. CONCLUDING REMARKS 297
REFERENCES 297 MULTICRITERIA SPATIAL PRICE NETWORKS: STATICS AND DYNAM-
ICS 299 ANNA NAGURNEY, JUNE DONG AND DING ZHANG 1. INTRODUCTION 299 2.
THE MULTICRITERIA SPATIAL PRICE MODEL 301 3. QUALITATIVE PROPERTIES 306
4. THE DYNAMICS 309 5. THE DISCRETE-TIME ALGORITHM 311 6. NUMERICAL
EXAMPLES 314 7. SUMMARY AND CONCLUSIONS 318 REFERENCES 319 NON REGULAER
DATA IN UNILATERAL VARIATIONAL PROBLEMS 323 PIRRO OPPEZZI 1.
INTRODUCTION 323 2. THE APPROACH BY TRUNCATION AND APPROXIMATION 324 3.
RENORMALIZED FORMULATION 328 4. MULTIVALUED OPERATORS AND MORE GENERAL
MEASURES 328 5. UNIQUENESS AND CONVERGENCE 330 REFERENCES 331
EQUILIBRIUM CONCEPTS IN TRANSPORTATION NETWORKS: GENERALIZED WARDROP
CONDITIONS AND VARIATIONAL FOR- MULATIONS 333 MASSIMO PAPPALARDO AND
MAURO PASSACANTANDO 1. INTRODUCTION 2. EQUILIBRIUM MODEL IN A TRAFFIC
NETWORK 333 334 XI REFERENCES 344 VARIATIONAL GEOMETRY AND EQUILIBRIUM
347 MICHAEL PATRIKSSON AND R. TYRRELL ROCKAFELLAR 1. INTRODUCTION 347 2.
VARIATIONAL INEQUALITIES AND NORMALS TO CONVEX SETS 349 3.
QUASI-VARIATIONAL INEQUALITIES AND NORMALS TO GENERAL SETS 352 4.
CALCULUS AND SOLUTION PERTURBATIONS 357 5. APPLICATION TO AN EQUILIBRIUM
MODEL WITH AGGREGATION 361 REFERENCES 367 ON THE CALCULATION OF
EQUILIBRIUM IN TIME DEPENDENT TRAFFIC NETWORKS 369 FABIO RACITI 1.
INTRODUCTION 369 2. CALCULATION OF EQUILIBRIA 370 3. THE ALGORITHM 371
4. APPLICATIONS AND EXAMPLES 372 5. CONCLUSIONS 376 REFERENCES 376
MECHANICAL EQUILIBRIUM AND EQUILIBRIUM SYSTEMS 379 TAMDS RAPCSDK 1.
INTRODUCTION 379 2. PHYSICAL MOTIVATION 380 3. STATEMENT OF THE
MECHANICAL FORCE EQUILIBRIUM PROBLEM 381 4. THE PRINCIPLE OF VIRTUAL
WORK 382 5. CHARACTERIZATION OF THE CONSTRAINTS 383 6. QUASI-VARIATIONAL
INEQUALITIES (QVI) 384 7. PRINCIPLE OF VIRTUAL WORK IN FORCE FIELDS
UNDER SCLERONOMIC AND HOLO- NOMIC CONSTRAINTS 385 8. DUAL FORM OF THE
PRINCIPLE OF VIRTUAL WORK IN FORCE FIELD UNDER SCLERO- NOMIC AND
HOLONOMIC CONSTRAINTS 388 9. PROCEDURE FOR SOLVING MECHANICAL
EQUILIBRIUM PROBLEMS 391 10. EXISTENCE OF SOLUTIONS 395 REFERENCES 397
XLL FALSE NUMERICAL CONVERGENCE IN SOME GENERALIZED NEWTON METHODS 401
STEPHEN M. ROBINSON 1. INTRODUCTION 401 2. SOME GENERALIZED NEWTON
METHODS 402 3. FALSE NUMERICAL CONVERGENCE 405 4. AN EXAMPLE 408 5.
AVOIDING FALSE NUMERICAL CONVERGENCE 411 REFERENCES 415 DISTANCE TO THE
SOLUTION SET OF AN INEQUALITY WITH AN INCREASING FUNCTION 417 ALEX M.
RUBINOV 1. INTRODUCTION 417 2. PRELIMINARIES 418 3. DISTANCE TO THE
SOLUTION SET OF THE INEQUALITY WITH AN ARBITRARY INCREAS- ING FUNCTION
420 4. DISTANCE TO THE SOLUTION SET OF THE INEQUALITY WITH AN ICAR
FUNCTION 423 5. INEQUALITIES WITH AN INCREASING FUNCTION DEFINED ON THE
ENTIRE SPACE 427 6. INEQUALITIES WITH A TOPICAL FUNCTION 429 REFERENCES
430 TRANSPORTATION NETWORKS WITH CAPACITY CONSTRAINTS 433 LAURA SCRIMALI
1. INTRODUCTION 433 2. WARDROP'S GENERALIZED EQUILIBRIUM CONDITION 434
3. A TRIANGULAER NETWORK 436 4. MORE ABOUT GENERALIZED EQUILIBRIUM
PRINCIPLE 438 5. CAPACITY CONSTRAINTS AND PARADOX 442 REFERENCES 443 |
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| genre_facet | Konferenzschrift |
| id | DE-604.BV022162808 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:19:11Z |
| indexdate | 2024-07-09T20:51:37Z |
| institution | BVB |
| isbn | 1402074700 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015377485 |
| oclc_num | 633747664 |
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| owner | DE-706 DE-11 |
| owner_facet | DE-706 DE-11 |
| physical | XII, 445 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Equilibrium problems and variational models ed. by Patrizia Daniele ... Dordrecht Kluwer 2003 XII, 445 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 68 Literaturangaben Variationsrechnung (DE-588)4062355-5 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Variationsrechnung (DE-588)4062355-5 s DE-604 Daniele, Patrizia Sonstige oth Nonconvex optimization and its applications 68 (DE-604)BV010085908 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015377485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Equilibrium problems and variational models Nonconvex optimization and its applications Variationsrechnung (DE-588)4062355-5 gnd |
| subject_GND | (DE-588)4062355-5 (DE-588)1071861417 |
| title | Equilibrium problems and variational models |
| title_auth | Equilibrium problems and variational models |
| title_exact_search | Equilibrium problems and variational models |
| title_exact_search_txtP | Equilibrium problems and variational models |
| title_full | Equilibrium problems and variational models ed. by Patrizia Daniele ... |
| title_fullStr | Equilibrium problems and variational models ed. by Patrizia Daniele ... |
| title_full_unstemmed | Equilibrium problems and variational models ed. by Patrizia Daniele ... |
| title_short | Equilibrium problems and variational models |
| title_sort | equilibrium problems and variational models |
| topic | Variationsrechnung (DE-588)4062355-5 gnd |
| topic_facet | Variationsrechnung Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015377485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
| work_keys_str_mv | AT danielepatrizia equilibriumproblemsandvariationalmodels |