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References
Asplund, E. andRockafellar, R. T., Gradients of convex functions,Trans. Amer. Math. Soc. 139 (1969), 443–467.
Attouch, H., Viscosity solutions of optimization problems. Epi-convergence and scaling,Sém. Anal. Convexe 22:8 (1992), 1–48.
Attouch, H. andAzé, D., Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method,Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 289–312.
Beer, G.,Topologies on Closed and Closed Convex Sets, Mathematics and its Applications268, Kluwer Academic Publishers Group, Dordrecht, 1993.
Benoist, J., Convergence de la dérivée de la régularisée Lasry-Lions,C. R. Acad. Sci. Paris Sér. I Math. 315 (1992), 941–944.
Deville, R., Godefroy, G., andZizler, V.,Smoothness and Renormings in Banach Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics64, Pitman, New York, 1993.
Ekeland, I. andLasry, J. M., On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface,Ann. of Math. 112 (1980), 283–319.
Fabian, M., Whitfield, J. H. M. andZizler, V., Norms with locally Lipschitzian derivatives,Israel J. Math. 44 (1983), 262–276.
Frontisi, J., Smooth partitions of unity in Banach spaces,Rocky Mountain J. Math. 25 (1995), 1295–1304.
Lasry, J. M. andLions, P. L., A remark on regularization in Hilbert spaces,Israel J. Math. 55 (1986), 257–266.
Lions, P. L.,Generalized Solutions of Hamilton-Jacobi Equations, Research Notes in Mathematics,69, Pitman (Advanced Publishing Program), Boston-London-Melbourne, 1982.
McLaughlin, D., Smooth partitions of unity and approximating norms in Banach spaces,Rocky Mountain J. Math. 25 (1995), 1137–1148.
McLaughlin, D., Poliquin, R., Vanderwerff, J. andZizler, V., Second-order Gâteaux differentiable bump functions and approximations in Banach spaces,Canad. J. Math. 45 (1993), 612–625.
Nemirovskiî, A. S. andSemenov, S. M., On polynomial approximation of functions on Hilbert Space.Mat. Sb. 92 (134) (1973), 257–281, 344 (Russian). English transl.:Math. USSR-Sb. 21 (1973), 255–277.
Poliquin, R., Vanderwerff, J. andZizler, V., Renormings and convex composite representations of functions,Preprint.
Rockafellar, R. T., Favorable classes of Lipschitz-continuous functions in subgradient optimization, inProgress in nondifferentiable optimization (Numinski, E. A., ed.), pp. 125–143, Internat. Inst. Appl. Systems Anal., Laxenburg, 1982.
Vanderwerff, J., Smooth approximations in Banach spaces,Proc. Amer. Math. Soc. 115 (1992), 113–120.
Zâlinescu, C., On uniformly convex functions,J. Math. Anal. Appl. 95 (1983), 344–374.
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Strömberg, T. On regularization in Banach spaces. Ark. Mat. 34, 383–406 (1996). https://doi.org/10.1007/BF02559552
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DOI: https://doi.org/10.1007/BF02559552