Cybernetics and Systems Analysis

, Volume 46, Issue 1, pp 51–55 | Cite as

Nonsmooth penalty and subgradient algorithms to solve the problem of projection onto a polytope

  • P. I. StetsyukEmail author
  • E. A. Nurminski

The least distance problem is considered for a convex hull of a finite family of vectors in a finite-dimensional Euclidian space. It is reduced to an equivalent nonsmooth optimization problem with a directly estimated penalty parameter for which subgradient algorithms with space dilation are proposed.


projection problem nonsmooth exact penalty functions r-algorithms 


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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Institute for Automation and Control ProcessesFar Eastern Branch of Russian Academy of SciencesVladivostokRussia

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