Wuhan University Journal of Natural Sciences

, Volume 1, Issue 3–4, pp 531–540 | Cite as

Parallel minimization algorithms by generalized subdifferentiability

  • C. Sutti
  • A. Peretti
Part II. Invited Lectures and Contributed Lectures 4. Numerical Parallel Algorithms


Recently a monotone generalized directional derivative has been introduced for Lipschitz functions. This concept has been applied to represent and optimize nonsmooth functions. The second application resulted relevant for parallel computing, by allowing to define minimization algorithms with high degree of inherent parallelism.

The paper presents first the teoretical background, namely the notions of monotone generalized directional derivative and monotone generalized subdifferential. Then it defines the tools for the procedures, that is a necessary optimality condition and a steepest descent direction. Therefore the minimization algorithms are outlined. Successively the used architectures and the performed numerical experience are described, by listing and commenting the tested functions and the obtained results.


Line Search Lipschitz Function Directional Derivative Minimization Algorithm Current Point 


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  1. [1]
    Demyanov V.F., Vasilev L.V. (1985), Non differentiable optimization, Opt. Soft. Inc. Publ. Div.Google Scholar
  2. [2]
    Peretti A., Sutti C. (1995), Monotone Convex and First Order Maps in Optimization of Nonsmooth Lipschitz Functions, Optimization, Vol. 33, pp. 105–117.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Rockafellar R.T. (1970), Convex Analysis.Google Scholar
  4. [4]
    Sutti C. (1993), On a monotone generalized derivative, Proc. of the Working Day on Math. Optim., Verona 92, Libr. Univ. Ed.Google Scholar
  5. [5]
    Sutti C. (1995), On the generalized differentiability, Optimization, Vol. 32, pp. 125–135.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Sutti C. (to appear), From Monotone Maps to Generalized Convex Functions.Google Scholar

Copyright information

© Springer 1996

Authors and Affiliations

  • C. Sutti
    • 1
  • A. Peretti
    • 1
  1. 1.Istituto di Matematica, Facoltà di Economia e CommercioUniversità di VeronaItaly

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