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

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Cybernetics and Systems Analysis Aims and scope

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.

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    P. I. Stetsyuk

  2. Institute for Automation and Control Processes, Far Eastern Branch of Russian Academy of Sciences, Vladivostok, Russia

    E. A. Nurminski

Authors
  1. P. I. Stetsyuk
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  2. E. A. Nurminski
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Correspondence to P. I. Stetsyuk.

Additional information

The study was financially supported by the joint Ukrainian-Russian project DFFD–F28.1/005 and RFFI–09–01–90413–Ukr_f_a “Subgradient methods of accelerated convergence in convex programming problems.”

Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 59–63, January–February 2010.

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Stetsyuk, P.I., Nurminski, E.A. Nonsmooth penalty and subgradient algorithms to solve the problem of projection onto a polytope. Cybern Syst Anal 46, 51–55 (2010). https://doi.org/10.1007/s10559-010-9182-5

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