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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 11, Pages 1991–1999 (Mi zvmmf567)  

This article is cited in 10 scientific papers (total in 10 papers)

Convergence of the suitable affine subspace method for finding the least distance to a simplex

E. A. Nurminski

Institute for Automation and Control Processes, Far East Division, Russian Academy of Sciences, ul. Radio 5, Vladivostok, 690041, Russia

Abstract: A minimum-length vector is found for a simplex in a finite-dimensional Euclidean space. The algorithm of successive projections onto affine subspaces containing suitable subsimplices of the initial simplex is shown to have a globally higher-than-linear convergence rate. Results of numerical experiments are presented.

Key words: projection, minimum-norm element, simplex.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:11, 1915–1922

Bibliographic databases:
UDC: 519.677
Received: 28.03.2005

Citation: E. A. Nurminski, “Convergence of the suitable affine subspace method for finding the least distance to a simplex”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 1991–1999; Comput. Math. Math. Phys., 45:11 (2005), 1915–1922

Citation in format AMSBIB
\by E.~A.~Nurminski
\paper Convergence of the suitable affine subspace method for finding the least distance to a simplex
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 11
\pages 1991--1999
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 11
\pages 1915--1922

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    This publication is cited in the following articles:
    1. Bagirov A.M., Ganjehlou A.N., Ugon J., Tor A.H., “Truncated codifferential method for nonsmooth convex optimization”, Pac J Optim, 6:3 (2010), 483–496  mathscinet  zmath  isi  elib
    2. Nurminski E.A., “Envelope stepsize control for iterative algorithms based on Fejer processes with attractants”, Optim. Methods Softw., 25:1 (2010), 97–108  crossref  mathscinet  zmath  isi  elib  scopus
    3. Bagirov A.M., Ugon J., “Codifferential method for minimizing nonsmooth DC functions”, J. Global Optim., 50:1 (2011), 3–22  crossref  mathscinet  zmath  isi  elib  scopus
    4. Gabidullina Z.R., “A theorem on strict separability of convex polyhedra and its applications in optimization”, J. Optim. Theory Appl., 148:3 (2011), 550–570  crossref  mathscinet  zmath  isi  elib  scopus
    5. Nurminskii E.A., Pozdnyak P.L., “Reshenie zadachi poiska naimenshego rasstoyaniya do politopa s ispolzovaniem graficheskikh uskoritelei”, Vychislitelnye tekhnologii, 16:5 (2011), 80–88  mathscinet  elib
    6. N. K. Arutyunova, A. M. Dulliev, V. I. Zabotin, “Algorithms for projecting a point onto a level surface of a continuous function on a compact set”, Comput. Math. Math. Phys., 54:9 (2014), 1395–1401  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. Fuduli A. Gaudioso M. Nurminski E.A., “A Splitting Bundle Approach For Non-Smooth Non-Convex Minimization”, Optimization, 64:5 (2015), 1131–1151  crossref  mathscinet  zmath  isi  elib  scopus
    8. Vorontsova E.A., Nurminski E.A., “Synthesis of Cutting and Separating Planes in a Nonsmooth Optimization Method”, Cybern. Syst. Anal., 51:4 (2015), 619–631  crossref  mathscinet  zmath  isi  elib  scopus
    9. Nurminski E.A., “Single-projection procedure for linear optimization”, J. Glob. Optim., 66:1, SI (2016), 95–110  crossref  mathscinet  zmath  isi  elib  scopus
    10. Vorontsova E., “Extended Separating Plane Algorithm and NSO-Solutions of PageRank Problem”, Discrete Optimization and Operations Research, Lecture Notes in Computer Science, 9869, eds. Kochetov Y., Khachay M., Beresnev V., Nurminski E., Pardalos P., Springer Int Publishing Ag, 2016, 547–560  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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