strong convergence

A strongly convergent projection and contraction algorithm with extrapolations from the past

  • Jianchao Bai
    • Categories Nonsmooth Optimization Tags , , ,

    This paper introduces a projection and contraction algorithm with extrapolation from the past for solving variational inequalities in Hilbert spaces. The proposed method reduces the number of operator evaluations per iteration from two to one by reusing past iterations. Under standard assumptions, we prove strong convergence of the generated sequence. Numerical experiments on solving large-scale … Read more

    On the Weak and Strong Convergence of a Conceptual Algorithm for Solving Three Operator Monotone Inclusions

  • Yunier Bello-Cruz
  • Oday Hazaimah
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Infinite Dimensional Optimization Tags , , , ,

    In this paper, a conceptual algorithm modifying the forward-backward-half-forward (FBHF) splitting method for solving three operator monotone inclusion problems is investigated. The FBHF splitting method adjusts and improves Tseng’s forward-backward-forward (FBF) split- ting method when the inclusion problem has a third-part operator that is cocoercive. The FBHF method recovers the FBF iteration (when this aforementioned … Read more

    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

    PROXIMAL THRESHOLDING ALGORITHM FOR MINIMIZATION OVER ORTHONORMAL BASES

  • Patrick L. Combettes
  • Jean-Christophe Pesquet
    • Categories Convex Optimization, Infinite Dimensional Optimization, Unconstrained Optimization Tags , , ,

    The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of … Read more