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Non-monotonous sequential subgradient projection algorithm for convex feasibility problem

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Abstract

The existing methods of projection for solving convex feasibility problem may lead to slow convergence when the sequences enter some narrow“corridor” between two or more convex sets. In this paper, we apply a technique that may interrupt the monotonity of the constructed sequence to the sequential subgradient projection algorithm to construct a non-monotonous sequential subgradient projection algorithm for solving convex feasibility problem, which can leave such corridor by taking a big step at different steps during the iteration. Under some suitable conditions, the convergence is proved.We also compare the numerical performance of the proposed algorithm with that of the monotonous algorithm by numerical experiments.

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Authors and Affiliations

  1. School of Management, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Ya-zheng Dang & Yan Gao

  2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China

    Jun-ling Sun

Authors
  1. Ya-zheng Dang
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  2. Jun-ling Sun
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  3. Yan Gao
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Corresponding author

Correspondence to Yan Gao.

Additional information

Supported by the National Science Foundation of China (No. 11171221), Natural Science Foundation of Shanghai (14ZR1429200), Innovation Program of Shanghai Municipal Education Commission (15ZZ074), Henan Province fundation frontier projec (No. 162300410226) Key Scientific research projectins of Henan Province(NO. 17b120001).

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Dang, Yz., Sun, Jl. & Gao, Y. Non-monotonous sequential subgradient projection algorithm for convex feasibility problem. Acta Math. Appl. Sin. Engl. Ser. 32, 1101–1110 (2016). https://doi.org/10.1007/s10255-016-0630-5

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  • DOI: https://doi.org/10.1007/s10255-016-0630-5

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