Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem

  • Charles Byrne
  • Yair Censor
  • Aviv Gibali
  • Simeon Reich
    • Categories Complementarity and Variational Inequalities, Convex Optimization, Nonlinear Optimization Short URL: https://optimization-online.org/?p=11691

    We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert space. This problem generalizes our Split Variational Inequality Problem (SVIP) [Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numerical Algorithms, accepted for publication, DOI 10.1007/s11075-011-9490-5]. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which under a given bounded linear transformation is a zero of another maximal monotone mapping. We present three iterative algorithms that solve such problems in Hilbert space, and establish weak convergence for one and strong convergence for the other two.

    Citation

    Technical Report, August 29, 2011.

    Article

    Download

    View Weak and Strong Convergence of Algorithms for the Split Common Null Point Problem