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Applications of Fixed‐Point and Optimization Methods to the Multiple‐Set Split Feasibility Problem

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  • Yonghong Yao
  • Rudong Chen
  • Giuseppe Marino
  • Yeong Cheng Liou

Abstract

The multiple‐set split feasibility problem requires finding a point closest to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. It generalizes the convex feasibility problem as well as the two‐set split feasibility problem. In this paper, we will review and report some recent results on iterative approaches to the multiple‐set split feasibility problem.

Suggested Citation

  • Yonghong Yao & Rudong Chen & Giuseppe Marino & Yeong Cheng Liou, 2012. "Applications of Fixed‐Point and Optimization Methods to the Multiple‐Set Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:927530
    DOI: 10.1155/2012/927530
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    References listed on IDEAS

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    1. Charles Byrne & Yair Censor, 2001. "Proximity Function Minimization Using Multiple Bregman Projections, with Applications to Split Feasibility and Kullback–Leibler Distance Minimization," Annals of Operations Research, Springer, vol. 105(1), pages 77-98, July.
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    Cited by:

    1. Kamonrat Sombut & Somyot Plubtieng, 2013. "Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Yonghong Yao & Yeong-Cheng Liou & Naseer Shahzad, 2012. "A Strongly Convergent Method for the Split Feasibility Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. Songnian He & Wenlong Zhu, 2012. "A Note on Approximating Curve with 1‐Norm Regularization Method for the Split Feasibility Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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