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An efficient simultaneous method for the constrained multiple-sets split feasibility problem

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  • Wenxing Zhang
  • Deren Han
  • Xiaoming Yuan

Abstract

The multiple-sets split feasibility problem (MSFP) captures various applications arising in many areas. Recently, by introducing a function measuring the proximity to the involved sets, Censor et al. proposed to solve the MSFP via minimizing the proximity function, and they developed a class of simultaneous methods to solve the resulting constrained optimization model numerically. In this paper, by combining the ideas of the proximity function and the operator splitting methods, we propose an efficient simultaneous method for solving the constrained MSFP. The efficiency of the new method is illustrated by some numerical experiments. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Wenxing Zhang & Deren Han & Xiaoming Yuan, 2012. "An efficient simultaneous method for the constrained multiple-sets split feasibility problem," Computational Optimization and Applications, Springer, vol. 52(3), pages 825-843, July.
    • Handle: RePEc:spr:coopap:v:52:y:2012:i:3:p:825-843
    DOI: 10.1007/s10589-011-9429-8
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    References listed on IDEAS

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    1. D. Han, 2007. "Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 227-243, February.
    2. Z. K. Jiang & X. M. Yuan, 2010. "New Parallel Descent-like Method for Solving a Class of Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 311-323, May.
    3. Bing-Sheng He, 2009. "Parallel splitting augmented Lagrangian methods for monotone structured variational inequalities," Computational Optimization and Applications, Springer, vol. 42(2), pages 195-212, March.
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    Cited by:

    1. X. Wang & S. Li & X. Kou & Q. Zhang, 2015. "A new alternating direction method for linearly constrained nonconvex optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 695-709, August.
    2. Seakweng Vong & Zhongsheng Yao, 2024. "Modified general splitting method for the split feasibility problem," Journal of Global Optimization, Springer, vol. 90(3), pages 711-726, November.
    3. Yuning Yang & Qingzhi Yang & Su Zhang, 2014. "Modified Alternating Direction Methods for the Modified Multiple-Sets Split Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 130-147, October.
    4. Hongjin He & Chen Ling & Hong-Kun Xu, 2015. "A Relaxed Projection Method for Split Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 213-233, July.

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