Maximal monotone relations and the second derivatives of nonsmooth functions
Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 3, pp. 167-184. 
@article{AIHPC_1985__2_3_167_0,
     author = {Rockafellar, R. T.},
     title = {Maximal monotone relations and the second derivatives of nonsmooth functions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {167--184},
     publisher = {Gauthier-Villars},
     volume = {2},
     number = {3},
     year = {1985},
     mrnumber = {797269},
     zbl = {0581.49009},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1985__2_3_167_0/}
}
TY  - JOUR
AU  - Rockafellar, R. T.
TI  - Maximal monotone relations and the second derivatives of nonsmooth functions
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1985
SP  - 167
EP  - 184
VL  - 2
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1985__2_3_167_0/
LA  - en
ID  - AIHPC_1985__2_3_167_0
ER  - 
%0 Journal Article
%A Rockafellar, R. T.
%T Maximal monotone relations and the second derivatives of nonsmooth functions
%J Annales de l'I.H.P. Analyse non linéaire
%D 1985
%P 167-184
%V 2
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1985__2_3_167_0/
%G en
%F AIHPC_1985__2_3_167_0
Rockafellar, R. T. Maximal monotone relations and the second derivatives of nonsmooth functions. Annales de l'I.H.P. Analyse non linéaire, Tome 2 (1985) no. 3, pp. 167-184. http://www.numdam.org/item/AIHPC_1985__2_3_167_0/

[1] A.D. Alexandrov, The existence almost everywhere of the second differential of a convex function and some associated properties of convex surfaces, Ucenye Zapiski Leningr. Gos. Univ. Ser. Mat., t. 37, 1939, p. 3-35 (in Russian).

[2] H. Attouch, Familles d'opérateurs maximaux monotones et mesurabilité, Annali di Matematica Pura et Applicata, t. 120, 1979, p. 35-111. | MR | Zbl

[3] H. Attouch and R.J.-B. Wets, A convergence for bivariate functions aimed at the convergence of saddle values, in Mathematical Theory of Optimization (P. Cecconi and T. Zolezzi, eds.), Springer-Verlag Lecture Notes in Math., t. 997, 1983. | MR | Zbl

[4] H. Attouch and R.J.-B. Wets, A convergence theory for saddle functions, Trans. Amer. Math. Soc., t. 226, 1983. | MR | Zbl

[5] J.P. Aubin, Lipschitz behavior of solutions to convex minimization problems, Math. of Op. Research, t. 9, 1984, p. 87-111. | MR | Zbl

[6] A. Auslender, Differential properties of the support function of the ∈-subdifferential of a convex function, Math. Programming, forthcoming. | MR | Zbl

[7] A. Auslender, Stability in mathematical programming with nondifferentiable data, SIAM J. Control Opt., t. 22, 1984, p. 239-254. | MR | Zbl

[8] F.H. Clarke, Nonsmooth Analysis and Optimization, Wiley-Interscience, 1983. | MR | Zbl

[9] F.H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc., t. 205, 1975, p. 247-262. | MR | Zbl

[10] F.H. Clarke, On the inverse function theorem, Pacific J. Math., t. 67, 1976, p. 97-102. | MR | Zbl

[11] B. Cornet, Regularity properties of normal and tangent cones, forthcoming. [12] S. DOLECKI, G. SALINETTI and R. J.-B. WETS, Convergence of functions: equi-semicontinuity, Trans. Amer. Math. Soc., t. 276, 1983, p. 409-429. | Zbl

[13] J.-B. Hiriart-Urruty, Approximating a second-order directional derivative for nonsmooth convex functions, SIAM J. Control Opt., t. 20, 1982, p. 783-807. | MR | Zbl

[14] J.-B. Hiriart-Urruty, Calculus rules on the approximate second-order directional derivative of a convex function, SIAM J. Control Opt., t. 22, 1984, p. 381-404. | MR | Zbl

[15] C. Lemarechal and E. Nurminski, Sur la différentiabilité de la fonction d'appui du sous-différentiel approaché, C. R. Acad. Sci. Paris, t. 290 Sér. A, 1980, p. 855-858. | Zbl

[16] F. Mignot, Contrôle dans les inéquations variationnelles elliptiques, J. Functional Anal., t. 22, 1976, p. 130-185. | MR | Zbl

[17] G.J. Minty, Monotone (nonlinear) operations in Hilbert space, Duke Math. J., t. 29, 1962, p. 341-346. | MR | Zbl

[18] J.-P. Penot, A characterization of tangential regularity, Nonlinear Anal., t. 5, 1981, p. 625-643. | MR | Zbl

[19] Yu.G. Reshetniak, Generalized derivatives and differentiability almost everywhere, Mat. Sbornik, t. 75, 1968, p. 323-334. | MR | Zbl

[20] R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl

[21] R.T. Rockafellar, Monotone operators associated with saddle functions and minimax problems, in Nonlinear Functional Analysis, Part I (F. E. Browder, ed.), Proc. of Symposia in Pure Math., Amer. Math. Soc., t. 18, 1970, p. 241-250. | MR | Zbl

[22] R.T. Rockafellar, Generalized subgradients in mathematical programming, in Mathematical Programming Bonn 1982 : The State of the Art : (A. Bachem et al., eds.), Springer-Verlag, Berlin, 1983, p. 368-380. | MR | Zbl

[24] R.T. Rockafellar and R.J.-B. Wets, Variational systems: An introduction, in Multifunctions and Integrands (G. Salinetti, ed.), Springer-Verlag Lecture Notes in Math. (1984). | MR

[25] S. Saks, Theory of the Integral, second revised edition, Hafner Publishing Co., New York, 1937. | JFM | Zbl

[26] G. Salinetti and R.J.-B. Wets, On the convergence of closed-valued measurable multifunctions, Trans. Amer. Math. Soc., t. 266, 1981, p. 275-289. | MR | Zbl

[27] R.J.-B. Wets, Convergence of convex function, variational inequalities and convex optimization problems, in Variational Inequalities and Complementarity Problems (R. Cottle, F. Giannessi and J.-L. Lions, eds.), Wiley, 1980, p. 405-419. | MR | Zbl