Variational inequalities and complementarity problems: theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily]
Gespeichert in:
| Format: | Tagungsbericht Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1980
|
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 408 S. graph. Darst. |
| ISBN: | 0471276103 |
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Datensatz im Suchindex
| _version_ | 1804116442974519296 |
|---|---|
| adam_text | Contents
1 The Work of G. Stampacchia in Variational Inequalities (J.L.
Lions) 1
1. Introduction 1
2. Variational inequalities 1
3. Application to potential theory 3
4. A number of variants and extensions 5
5. The obstacle problem 8
6. An abstract regularity theorem. Application to the ob¬
stacle problem 11
7. An inequality for the obstacle problem 13
8. Elasto-plastic problem 15
9. Hodograph method and VI 17
10. Fourth-order VI 19
11. Infiltration in porous media 21
12. Conclusion 22
2 Variational Inequalities and Free-Boundary Problems (C.
Baiocchi) 25
1. The simplest elliptic free-boundary problem. Inter¬
connections with variational inequalities 25
2. Some other examples of FB problems 28
3. Variational approach for problem 2 31
3 Existence of a Ground State in Non-Linear Equations of the
Klein-Gordon Type (//. Berestyckiand PL. Lions) 35
1. Introduction 35
2. Proof of theorem 1.1 37
3. Discussion on the hypotheses and indications on other
methods 45
4 Some Variational Problems of the Thomas-Fermi Type (//.
Brezis) 53
1. Introduction 53
xiii
xiv
2. The variational formulation and the Euler-Lagrange
formulation. Conditions for equivalence 56
3. A direct approach for solving the Euler-Lagrange equa¬
tion 61
4. A min-max principle for the Lagrange multiplier 69
5 Implicit Complementarity Problems and Quasi-Variational
Inequalities (/. Capuzzo Dolcetta and U. Mosco) 75
1. Introduction 75
2. The strong ICP 75
3. QVIs and the weak ICP 76
4. The Young-Fenchel equation and QVIs in duality 78
5. Existence of solutions 79
6. Remarks on stability, numerical approximation, and
algorithms 83
6 A Minimum Time Problem (R. Conti) 89
1. Introduction 89
2. Trasfer Sets 89
3. The function T 91
4. Regularity of T 92
5. The synthesis problem 93
7 Some Recent Developments in Linear Complementarity Theory
(R. W. Cottle) 97
1. Introduction 97
2. Complementary submatrices and cones 97
3. Existence: a characterization of the class Po n Q 99
4. Stability: topological properties of Q 100
5. Degeneracy: least-index rules for its resolution 100
6. Computational complexity: worst-case behaviour of
complementarity algorithms 102
8 Some Stochastic Strategies in Optimization Problems (M.
Cugiani) 105
1. Introduction 105
2. Deterministic strategies 106
3. Probabilistic methods 113
4. The clustering approach 114
5. The i// function approach 115
6. Global optimization via stochastic models 120
9 Pricing Underemployed Capacity in a Linear Economic Model
(G.B. Dantzig and PL Jackson) 127
1. Introduction 127
2. The method 127
3. Summary 134
XV
10 The Dam Problem with Variable Permeability (A. Friedman) 135
1. The Stationary problem 135
2. Non-steady flow 138
11 Stochastic Control with Partial Observations (A. Friedman) 143
1. Introduction 143
2. The problem 143
3. Imbedding the problem and deriving the quasi-variational
inequalities 145
12 Theorems of Alternative, Quadratic Programs, and Complemen¬
tarity Problems (F. Giannessi) 151
1. Introduction 151
2. Theorems of alternative for non-linear systems 151
3. Applications to extremum problems and to variational
inequalities 159
4. Applications to vector extremum problems 165
5. Concave auxiliary function for quadratic programs 167
6. Decomposition of convex quadratic programs 169
7. Decomposition of non-convex quadratic programs 175
8. Decomposition of a class of complementarity pro¬
blems 177
9. Numerical Examples 181
13 An Existence Result for the Global Newton Method (F.J. Gould
and C.P. Schmidt) 187
14 The Smoothness of Free Boundaries Governed by Elliptic
Equations and Systems (D. Kinderlehrer) 195
1. Introduction 195
2. Hodograph mappings 198
3. The obstacle problem: a single second-order equation .... 201
4. The confined plasma 202
5. The double membrane 203
6. The smoothness of the liquid edge 207
7. Higher order equations: the deflection of a thin plate .... 207
8. An extension of a theorem of Hans Lewy 210
15 A Survey of Complementarity Theory (C.E. Lemke) 213
1. Introduction 213
2. Some equivalences 214
3. The linear complementarity problem 217
4. Pivoting 218
5. Some classes of matrices. Existence and uniqueness in
LCP 220
6. Classes of matrices and CPS 223
7. Some relations between LCP and LP 223
8. Models and applications of LCP 224
xvi
9. CAM developments 227
10. Simplicial approximation methods (SAM) 227
11. Solutions to systems of equations 230
12. Continuation methods 235
16. An Estimate of the Lipschitz Norm of Solutions of Variational
Inequalities and Applications (P.L. Lions) 241
1. Introduction 241
2. The main result 242
3. An application to the elastic-plastic problem 246
17 The Complementarity Problem for Maximal Monotone Multi-
functions (L. McLinden) 251
1. Introduction 251
2. Problem statement and examples 252
3. Existence and properties of trajectories of approximate
solutions 259
4. Stability, continuity, and generic properties 268
18 On Some Non-Linear Quasi-Variational Inequalities and Implicit
Complementarity Problems in Stochastic Control Theory
(U. Mosco) 271
1. Introduction 271
2. Strong regularity of weak solutions 272
3. Proof of proposition 1 277
4. Iterative algorithms 281
19 On Two Variational Inequalities Arising from a Periodic Visco-
elastic Unilateral Problem (M. Raous) 285
1. Introduction 285
2. The mechanical problem 285
3. The constitutive law 288
4. Functional scheme 289
5. The equations 290
6. Discretization and numerical treatment 293
7. Example 296
8. Other aspects and references 301
20 Lagrange Multipliers and Variational Inequalities (R.T.
Rockafellar) 303
1. Introduction 303
2. The general problem 304
3. Discretization 306
4. Complementarity 309
5. Linearity versus non-linearity 312
6. Generalization to multifunctions 315
7. Penalty-duality methods 316
8. Proximal method of multipliers 319
xvii
21 A Numerical Approach to the Solution of Some Variational
Inequalities (F. Scarpini) 323
1. Introduction 324
2. Algorithms 326
3. Unilateral Dirichlet problems related to some operators . . 334
22 Error Estimates for the Finite Element Approximation of Some
Variational Inequalities (F. Scarpini) 339
1. Introduction 339
2. A first example of stationary variational inequality 339
3. A second example of stationary variational inequality ... 342
4. A parabolic evolution inequality of type I 343
5. A parabolic evolution inequality of type II 345
23 Bifurcation Analysis of the Free Boundary of a Confined Plasma
(/. Sijbrand) 349
1. Introduction 349
2. Method of solution 350
3. Example 354
24 Mathematical Problems in Plasticity Theory (R. Temam) 357
1. Introduction 357
2. The model problem for limit analysis 357
3. The model problem for deformation theory 367
25 Convergence of Convex Functions, Variational Inequalities,
and Convex Optimization Problems {R.J.B. Wets) 375
1. Introduction 375
2. Convergence of convex functions 375
3. Convergence of sequences of closed convex sets 377
4. Characterizing e-convergence 380
5. Relations between e-convergence and p-convergence 388
6. A further characterization of e-convergence 394
7. Convergence of the infima 398
8. Convergence of optimal solutions 400
Subject Index 405
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| spelling | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] ed. by R. W. Cottle ... Chichester [u.a.] Wiley 1980 XVII, 408 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd rswk-swf Variationsungleichung (DE-588)4187420-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1978 Erice gnd-content Variationsungleichung (DE-588)4187420-1 s Minimum-Maximum-Prinzip (DE-588)4170060-0 s DE-604 Cottle, Richard 1934- Sonstige (DE-588)170020169 oth International School of Mathematics 1978 Erice Sonstige (DE-588)812438-3 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001301938&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| subject_GND | (DE-588)4170060-0 (DE-588)4187420-1 (DE-588)1071861417 |
| title | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] |
| title_auth | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] |
| title_exact_search | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] |
| title_full | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] ed. by R. W. Cottle ... |
| title_fullStr | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] ed. by R. W. Cottle ... |
| title_full_unstemmed | Variational inequalities and complementarity problems theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] ed. by R. W. Cottle ... |
| title_short | Variational inequalities and complementarity problems |
| title_sort | variational inequalities and complementarity problems theory and applications proceedings of an international school of mathematics devoted to variational inequalities and complementarity problems in mathematical physics and economics held from 19 to 30 june 1978 the site for the meeting was the ettore majorana centre for scientific culture in erice sicily |
| title_sub | theory and applications ; [proceedings of an International School of Mathematics devoted to Variational Inequalities and Complementarity Problems in Mathematical Physics and Economics, held from 19 to 30 June 1978 ; the site for the meeting was the 'Ettore Majorana' Centre for Scientific Culture in Erice, Sicily] |
| topic | Minimum-Maximum-Prinzip (DE-588)4170060-0 gnd Variationsungleichung (DE-588)4187420-1 gnd |
| topic_facet | Minimum-Maximum-Prinzip Variationsungleichung Konferenzschrift 1978 Erice |
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