@article{AIHPC_1993__10_3_289_0, author = {Attouch, H. and Aze, D.}, title = {Approximation and regularization of arbitrary functions in {Hilbert} spaces by the {Lasry-Lions} method}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {289--312}, publisher = {Gauthier-Villars}, volume = {10}, number = {3}, year = {1993}, mrnumber = {1230710}, zbl = {0780.41021}, language = {en}, url = {http://archive.numdam.org/item/AIHPC_1993__10_3_289_0/} }
TY - JOUR AU - Attouch, H. AU - Aze, D. TI - Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method JO - Annales de l'I.H.P. Analyse non linéaire PY - 1993 SP - 289 EP - 312 VL - 10 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPC_1993__10_3_289_0/ LA - en ID - AIHPC_1993__10_3_289_0 ER -
%0 Journal Article %A Attouch, H. %A Aze, D. %T Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method %J Annales de l'I.H.P. Analyse non linéaire %D 1993 %P 289-312 %V 10 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPC_1993__10_3_289_0/ %G en %F AIHPC_1993__10_3_289_0
Attouch, H.; Aze, D. Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method. Annales de l'I.H.P. Analyse non linéaire, Volume 10 (1993) no. 3, pp. 289-312. http://archive.numdam.org/item/AIHPC_1993__10_3_289_0/
[1] Fréchet differentiability of convex functions, Acta Math., Vol. 121, 1968, pp. 31-47. | MR | Zbl
,[2] Variational Convergences for Functions and Operators,, Applicable Mathematics SeriesPitman London, 1984. | MR | Zbl
,[3] On continuity properties of the partial Legendre-Fenchel transform: convergence of sequences of augmented Lagrangians functions, Moreau-Yosida approximates and subdifferential operators, Fermat days 85: Mathematicsfor Optimization, J.-B. HIRIART-URRUTY Ed., North-Holland Amsterdam, 1986, pp. 1-42. | MR
, and ,[4] Epigraphical analysis, Analyse non linéaire, H. ATTOUCH, J.-P. AUBIN, F. H. CLARKE and I. EKELAND Eds., Gauthier-Villars, Paris, 1989, pp. 73-100. | EuDML | Numdam | MR | Zbl
and ,[5] Uniformly convex and uniformly smooth convex functions (submitted). | Zbl
and ,[6] Contribution à la théorie de Morse en dimension finie, Thèse de 3e cycle, Université de Paris-IX, 1978.
,[7] Approximation and decomposition properties of some classes of locally d.c. functions, Math. Progr., Vol. 41, 1989, pp. 195-227. | MR | Zbl
and ,[8] Towards minimal assumptions for the infimal convolution regularization, J. of Approx. Theory, Vol. 64, 1991, pp. 245-270. | MR | Zbl
, and ,[9] Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. | MR | Zbl
,[10] Optimization and Nonsmooth Analysis, J. Wiley, New York, 1983. | MR | Zbl
,[11] Problèmes variationnels non convexes en dualité, C. R. Acad. Sci. Paris, 291, Series I, 1980, pp. 493-497. | MR | Zbl
and ,[12] A general formula on the conjugate of the difference of functions, Can. Math. Bull., Vol. 29, 1986, pp. 482-485. | MR | Zbl
,[13] Moreau's decomposition Theorem revisited, Analyse non linéaire, H. ATTOUCH, J.-P. AUBIN, F. H. CLARKE, I. EKELAND Eds., Gauthier-Villars, Paris, 1989. | Numdam | Zbl
and ,[14] Extension of Lipschitz functions, J. Math. Anal. Appl., Vol. 72, 1980, pp. 539-554. | MR | Zbl
,[15] Lipschitz r-continuity of the approximate subdifferential of a convex function, Math. Scand., Vol. 47, 1980, pp. 123-134. | MR | Zbl
,[16] A remark on regularization in Hilbert spaces, Israel Journal of Mathematics, Vol. 55, 1986, pp. 257-266. | MR | Zbl
and ,[17] Fonctionnelles convexes, Lecture Notes, Collège de France, Paris, 1967.
,[18] Proximité et dualité dans un espace Hilbertien, Bull. Soc. Math. Fr., Vol. 93, 1965, pp. 273-299. | Numdam | MR | Zbl
,[19] Semi-groups of nonlinear contractions in Hilbert spaces, in Problems in Nonlinear Analysis, Edizioni Cremonese, Roma, 1971, pp. 343-430. | MR | Zbl
,[20] Analyse convexe et théorie de Morse, Thèse de 3e cycle, Université de Paris-IX, 1982.
,[21] Convex Analysis, Princeton University Press, 1966. | MR | Zbl
,[22] Generalized directional derivatives and subgradients of nonconvex functions, Canadian J. Math., Vol. 32, 1980, pp. 157-180. | MR | Zbl
,[23] On paraconvex multifunctions, Proceedings of III Symposium uber Operation Research, Mannheim, Sept. 1978, pp. 539-546. | MR | Zbl
,[24] On uniformly convex functionals, Vest. Mosk. Univ., Vol. 3, 1978, pp. 12-23 (Russian). | MR | Zbl
, and ,[25] Differentiable functions on Banach spaces with lipschitz derivative, J. Differential Geometry, Vol. 8, 1973, pp. 135-152. | MR | Zbl
,[26] Functional analysis, third ed., Springer, Berlin, Heidelberg, New York, 1971. | Zbl
,[27] On uniformly convex functions, Jour. Math. Anal. Appl., Vol. 95, 1983, pp. 344-374. | MR | Zbl
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