Cyclic Coordinate-Update Algorithms for Fixed-Point Problems: Analysis and Applications

Coordinate Friendly Structures, Algorithms and Applications

This paper focuses on the coordinate update method, which is useful for solving large-sized problems involving linear and nonlinear mappings, and smooth and nonsmooth functions. It decomposes a problem into simple subproblems, where each subproblem updates one, or a small block of, variables. The coordinate update method sits at a high level of abstraction and includes many special cases such a...

Equilibrium problems and fixed point problems for nonspreading-type mappings in hilbert space

In this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in Hilbert space. A strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. The main result of this paper extendthe results obtain...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings

In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p

On Unbounded Delays in Asynchronous Parallel Fixed-Point Algorithms

The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies the convergence of the asynchronous parallel algorithm ARock under potentially unbounded delays. ARock is a general asynchronous algorithm that has many app...