resolvent operator

A new explicit iterative algorithm for solving split variational inclusion and fixed point problem for the infinite family of nonexpansive operators

  • Zhihui Xu
  • Cuijie Zhang
    • Categories Complementarity and Variational Inequalities Tags , , , ,

    In this paper, we introduce a new explicit iterative algorithm for finding a solution of split variational inclusion problem over the common fixed points set of a infinite family of nonexpansive mappings in Hilbert spaces. To reach this goal, the iterative algorithms which combine Tian’s method with some fixed point technically proving methods are utilized … Read more

    Linearized Alternating Direction Method with Gaussian Back Substitution for Separable Convex Programming

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , ,

    Recently, we have proposed to combine the alternating direction method (ADM) with a Gaussian back substitution procedure for solving the convex minimization model with linear constraints and a general separable objective function, i.e., the objective function is the sum of many functions without coupled variables. In this paper, we further study this topic and show … Read more

    A contraction method with implementable proximal regularization for linearly constrained convex programming

  • Bingsheng He
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , ,

    The proximal point algorithm (PPA) is classical, and it is implicit in the sense that the resulting proximal subproblems may be as difficult as the original problem. In this paper, we show that with appropriate choices of proximal parameters, the application of PPA to the linearly constrained convex programming can result in easy proximal subproblems. … Read more