Stable approximations of set-valued maps

Jean-Pierre Aubin; Roger J. Wets

Annales de l'I.H.P. Analyse non linéaire (1988)

  • Volume: 5, Issue: 6, page 519-535
  • ISSN: 0294-1449

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Aubin, Jean-Pierre, and Wets, Roger J.. "Stable approximations of set-valued maps." Annales de l'I.H.P. Analyse non linéaire 5.6 (1988): 519-535. <http://eudml.org/doc/78163>.

@article{Aubin1988,
author = {Aubin, Jean-Pierre, Wets, Roger J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {graph convergence; nonlinear inlusions; stability; contingent derivative},
language = {eng},
number = {6},
pages = {519-535},
publisher = {Gauthier-Villars},
title = {Stable approximations of set-valued maps},
url = {http://eudml.org/doc/78163},
volume = {5},
year = {1988},
}

TY - JOUR
AU - Aubin, Jean-Pierre
AU - Wets, Roger J.
TI - Stable approximations of set-valued maps
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1988
PB - Gauthier-Villars
VL - 5
IS - 6
SP - 519
EP - 535
LA - eng
KW - graph convergence; nonlinear inlusions; stability; contingent derivative
UR - http://eudml.org/doc/78163
ER -

References

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  1. H. Attouch, Variational Convergence for Functions and Operators, Applicable Mathematics Series Pitman, London, 1984. Zbl0561.49012MR773850
  2. J.-P. Aubin, Approximation of Elliptic Boundary-Value Problems, Wiley-Intersecience, 1972. Zbl0248.65063MR478662
  3. J.-P. Aubin, Contingent Derivatives of Set-Valued Maps and Existence of Solutions to Nonlinear Inclusions and Differential Inclusions, Advances in Mathematics, Supplementary studies, L. NACHBIN Ed., 1981, pp. 160-232. Zbl0484.47034MR634239
  4. J.-P. Aubin, Comportement lipschitzien des solutions de problèmes de minimisation convexes, C.R. Acad. Sci. Paris, T. 295, Series I, 1982, pp. 235-238. Zbl0503.49022MR681586
  5. J.-P. Aubin, Comportement lipschitzien des solutions de problèmes de minimisation convexes. In Non linear Parial Differential Equations and their Applications, Collège de France seminar IV, 81/82, 1983, pp. 1-18, Research Notes in Mathematics, Pitman, London. Zbl0523.49012MR716510
  6. J.-P. Aubin, Lipschitz Behavior of Solutions to Convex Minimization Problems, Mathematics of Operations Research, Vol. 8, 1984, pp. 87-111. Zbl0539.90085MR736641
  7. J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag; Grundlehren der Mathematische Wissenschaften, Vol. 264, 1984, pp. 1-342. Zbl0538.34007MR755330
  8. J.-P. Aubin and F.H. Clarke, Monotone Invariant Solutions to Differential Inclusions, J. London Mathematical Society, Vol. 16, 1977, pp. 357-366. Zbl0405.34049MR486742
  9. J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984. Zbl0641.47066MR749753
  10. J.-P. Aubin and H. Frankowska, On inverse Function Theorems for Set-Valued Maps, J. Mathématiques pures et appliquées T. 66, 1987, pp. 71-89. Zbl0643.46033MR884814
  11. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, 1983. Zbl0582.49001MR709590
  12. Sz. Dolecki, G. Salinetti and R. Wets, Convergence of Functions: Equi-Semicontinuity, Transactions of the American Mathematical Society, Vol. 276, pp. 409-429. Zbl0504.49006MR684518
  13. I. Ekeland, On the Variational Principle, J. Mathematical Analysis and Applications, Vol. 47, 1974, pp. 324-353. Zbl0286.49015MR346619
  14. H. Frankowska, 1974, Inclusions adjointes associées aux trajectoires minimales d'une inclusion différentielle, C.R. Acad. Sci. Paris, T. 206, Series I, 1983. Zbl0532.49024
  15. H. Frankowska, A Viability Approach to the Skorohod Problem, Stochastics, Vol. 14, 1985, pp. 227-244. Zbl0601.60059MR800245
  16. H. Frankowska, An Open Mapping Principle for Set-Valued Maps, Journal M. A. Appl., Vol. 127, 1987, pp. 172-180. Zbl0643.46034MR904219
  17. S. Robinson, Regularity and Stability for Convex Multivalued Functions, Mathematics of Operations Research, Vol. 1, 1976, pp. 130-143. Zbl0418.52005MR430181
  18. R.T. Rockafellar, Monotone Processes of Convex and Concave Type, Memoirs of American Mathematical Society, No. 77, 1967. Zbl0189.19602MR225231
  19. R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970. Zbl0193.18401MR274683
  20. R.T. Rockafellar, La théorie des sous-gradients, Presses de l'Université de Montréal, Montréal, 1979. MR531033
  21. G. Salinetti and R. Wets, On the Relation Between Two Types of Convergence for Convex Functions, J. Mathematical Analysis and Applications, Vol. 60, 1977, pp. 211-226. Zbl0359.54005MR479398
  22. C. Ursescu, Multifunctions with Closed Convex Graph, Czechoslovakia Mathematics J., Vol. 25, 1975, 438-441. Zbl0318.46006MR388032

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