Smoothness of Nonsmooth Functions
Our aim is to show that most well-known classes of nondifferentiable functions are in some sense quite smooth. Nonsmooth analysis (for short, NSA) is one of most attractive and promising areas in modern mathematics. A lot of new profound results have been obtained and much more seem to come (see, e.g., [1–6] and References therein).
KeywordsOrder Approximation Directional Derivative Concave Function Open Convex Nonsmooth Analysis
Unable to display preview. Download preview PDF.
- R.T. Rockafellar. “Convex analysis”. Princeton Math. Ser. 28 (1970).Google Scholar
- B.N. Pschenichnyi. “Convex analysis and extrema problems”. Nauka, Moscow (1980).Google Scholar
- F.H. Clarke. “Nonsmooth analysis and optimization”. J. Wiley Interscience, New York (1983).Google Scholar
- A.D. Ioffe, V.M. Tikhomirov. “Theory of extremal problems”. North-Holland Publ. Co., Amsterdam-New York (1979).Google Scholar
- B.S. Mordukhovich. “Approximation methods in problems of optimization and control”. Nauka Publ., Moscow (1988).Google Scholar
- V.F. Demyanov. “On codifferentiable functions”. Vestnik of Leningrad University, N.2 (8) (1988), pp. 22–26.Google Scholar
- V.F. Demyanov. “Continuous generalized gradients for nonsmooth functions”. In Lecture Notes in Economics and Mathematical Systems, vol. 304 (eds. A. Kurzhanski, K. Neumann, D. Pallaschke ), Springer-Verlag, (1988), pp. 24–27.Google Scholar