Smoothness of Nonsmooth Functions

  • V. F. Dem’yanov
Part of the Ettore Majorana International Science Series book series (EMISS, volume 43)


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).


Order Approximation Directional Derivative Concave Function Open Convex Nonsmooth Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R.T. Rockafellar. “Convex analysis”. Princeton Math. Ser. 28 (1970).Google Scholar
  2. [2]
    B.N. Pschenichnyi. “Convex analysis and extrema problems”. Nauka, Moscow (1980).Google Scholar
  3. [3]
    F.H. Clarke. “Nonsmooth analysis and optimization”. J. Wiley Interscience, New York (1983).Google Scholar
  4. [4]
    A.D. Ioffe, V.M. Tikhomirov. “Theory of extremal problems”. North-Holland Publ. Co., Amsterdam-New York (1979).Google Scholar
  5. [5]
    B.S. Mordukhovich. “Approximation methods in problems of optimization and control”. Nauka Publ., Moscow (1988).Google Scholar
  6. [6]
    V.F. Demyanov, A.M. Rubinov. “Quasidifferential calculus”. Optimization Software Inc., New York (1986).CrossRefMATHGoogle Scholar
  7. [7]
    V.F. Demyanov. “On codifferentiable functions”. Vestnik of Leningrad University, N.2 (8) (1988), pp. 22–26.Google Scholar
  8. [8]
    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

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • V. F. Dem’yanov
    • 1
  1. 1.Dept. of Applied MathematicsLeningrad State UnivLeningradUSSR

Personalised recommendations