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Parallel Method of Pseudoprojection for Linear Inequalities

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Parallel Computational Technologies (PCT 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 910))

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Abstract

This article presents a new iterative method for finding an approximate solution of a linear inequality system. This method uses the notion of pseudoprojection which is a generalization of the operation of projecting a point onto a closed convex set in Euclidean space. Pseudoprojecting is an iterative process based on Fejer approximations. The proposed pseudoprojection method is amenable to parallel implementation exploiting the subvector method, which is also presented in this article. We prove both the subvector method correctness and the convergence of the pseudoprojection method.

I. Sokolinskaya—The study has been partially supported by the RFBR according to research project No. 17-07-00352-a and by the Government of the Russian Federation according to Act 211 (contract No. 02.A03.21.0011).

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Notes

  1. 1.

    Here \(\mathrm {dist} (x,P) = \inf \left\{ {\left\| {x - y} \right\| :y \in P} \right\} \).

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Authors and Affiliations

  1. South Ural State University, 76 Lenin prospekt, Chelyabinsk, 454080, Russia

    Irina Sokolinskaya

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  1. Irina Sokolinskaya
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Correspondence to Irina Sokolinskaya .

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Editors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Leonid Sokolinsky

  2. South Ural State University, Chelyabinsk, Russia

    Mikhail Zymbler

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Sokolinskaya, I. (2018). Parallel Method of Pseudoprojection for Linear Inequalities. In: Sokolinsky, L., Zymbler, M. (eds) Parallel Computational Technologies. PCT 2018. Communications in Computer and Information Science, vol 910. Springer, Cham. https://doi.org/10.1007/978-3-319-99673-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-99673-8_16

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