Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method
Attouch, H. ; Aze, D.
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993), p. 289-312 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_1993__10_3_289_0,
     author = {Attouch, H\'edy and Aze, Dominique},
     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},
     volume = {10},
     year = {1993},
     pages = {289-312},
     mrnumber = {1230710},
     zbl = {0780.41021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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, Tome 10 (1993) pp. 289-312. http://gdmltest.u-ga.fr/item/AIHPC_1993__10_3_289_0/

[1] E. Asplund, Fréchet differentiability of convex functions, Acta Math., Vol. 121, 1968, pp. 31-47. | MR 231199 | Zbl 0162.17501

[2] H. Attouch, Variational Convergences for Functions and Operators,, Applicable Mathematics SeriesPitman London, 1984. | MR 773850 | Zbl 0561.49012

[3] H. Attouch, D. Azé and R.J.B. Wets, 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 874359

[4] H. Attouch and R.J.B. Wets, Epigraphical analysis, Analyse non linéaire, H. ATTOUCH, J.-P. AUBIN, F. H. CLARKE and I. EKELAND Eds., Gauthier-Villars, Paris, 1989, pp. 73-100. | Numdam | MR 1019109 | Zbl 0676.49003

[5] D. Azé and J.-P. Penot, Uniformly convex and uniformly smooth convex functions (submitted). | Zbl 0870.49010

[6] M. Bougeard, Contribution à la théorie de Morse en dimension finie, Thèse de 3e cycle, Université de Paris-IX, 1978.

[7] J.-P. Penot and M. Bougeard, Approximation and decomposition properties of some classes of locally d.c. functions, Math. Progr., Vol. 41, 1989, pp. 195-227. | MR 945661 | Zbl 0666.49005

[8] M. Bougeard, J.-P. Penot and A. Pommelet, Towards minimal assumptions for the infimal convolution regularization, J. of Approx. Theory, Vol. 64, 1991, pp. 245-270. | MR 1094438 | Zbl 0759.49003

[9] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland, Amsterdam, 1973. | MR 348562 | Zbl 0252.47055

[10] F.H. Clarke, Optimization and Nonsmooth Analysis, J. Wiley, New York, 1983. | MR 709590 | Zbl 0582.49001

[11] I. Ekeland and J.-M. Lasry, Problèmes variationnels non convexes en dualité, C. R. Acad. Sci. Paris, 291, Series I, 1980, pp. 493-497. | MR 599991 | Zbl 0448.90063

[12] J.-B. Hiriart-Urruty, A general formula on the conjugate of the difference of functions, Can. Math. Bull., Vol. 29, 1986, pp. 482-485. | MR 860858 | Zbl 0608.90087

[13] J.-B. Hiriart-Urruty and Ph. Plazanet, 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 0675.90093

[14] J.-B. Hiriart-Urruty, Extension of Lipschitz functions, J. Math. Anal. Appl., Vol. 72, 1980, pp. 539-554. | MR 593233 | Zbl 0455.26006

[15] J.-B. Hiriart-Urruty, Lipschitz r-continuity of the approximate subdifferential of a convex function, Math. Scand., Vol. 47, 1980, pp. 123-134. | MR 600082 | Zbl 0426.26005

[16] J.-M. Lasry and P.-L. Lions, A remark on regularization in Hilbert spaces, Israel Journal of Mathematics, Vol. 55, 1986, pp. 257-266. | MR 876394 | Zbl 0631.49018

[17] J.-J. Moreau, Fonctionnelles convexes, Lecture Notes, Collège de France, Paris, 1967.

[18] J.-J. Moreau, Proximité et dualité dans un espace Hilbertien, Bull. Soc. Math. Fr., Vol. 93, 1965, pp. 273-299. | Numdam | MR 201952 | Zbl 0136.12101

[19] A. Pazy, Semi-groups of nonlinear contractions in Hilbert spaces, in Problems in Nonlinear Analysis, Edizioni Cremonese, Roma, 1971, pp. 343-430. | MR 291877 | Zbl 0228.47038

[20] A. Pommelet, Analyse convexe et théorie de Morse, Thèse de 3e cycle, Université de Paris-IX, 1982.

[21] R.T. Rockafellar, Convex Analysis, Princeton University Press, 1966. | MR 1451876 | Zbl 0193.18401

[22] R.T. Rockafellar, Generalized directional derivatives and subgradients of nonconvex functions, Canadian J. Math., Vol. 32, 1980, pp. 157-180. | MR 571922 | Zbl 0447.49009

[23] S. Rolewicz, On paraconvex multifunctions, Proceedings of III Symposium uber Operation Research, Mannheim, Sept. 1978, pp. 539-546. | MR 541221 | Zbl 0403.49021

[24] A.A. Vladimirov, Yu.E. Nesterov and Yu.N. Chekanov, On uniformly convex functionals, Vest. Mosk. Univ., Vol. 3, 1978, pp. 12-23 (Russian). | MR 516874 | Zbl 0442.47046

[25] J.C. Wells, Differentiable functions on Banach spaces with lipschitz derivative, J. Differential Geometry, Vol. 8, 1973, pp. 135-152. | MR 370640 | Zbl 0289.58005

[26] K. Yosida, Functional analysis, third ed., Springer, Berlin, Heidelberg, New York, 1971. | Zbl 0217.16001

[27] C. Zalinescu, On uniformly convex functions, Jour. Math. Anal. Appl., Vol. 95, 1983, pp. 344-374. | MR 716088 | Zbl 0519.49010