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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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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DOI: https://doi.org/10.1007/s10559-010-9182-5