A stochastic coordinate descent splitting primal-dual fixed point algorithm and applications to large-scale composite optimization

TL;DR

This paper introduces a stochastic coordinate descent splitting primal-dual fixed point algorithm for large-scale convex optimization, leveraging proximity operators and randomized iterations to ensure convergence.

Contribution

It presents a novel stochastic coordinate descent algorithm based on fixed point methods for convex optimization problems involving composite functions.

Findings

Algorithm converges under certain conditions

Applicable to large-scale composite optimization problems

Utilizes randomized Krasnosel'skii-Mann iterations

Abstract

We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators, which is is inspired by recent results of Chen, Huang and Zhang. With the idea of coordinate descent, we design a stochastic coordinate descent splitting primal- dual fixed point algorithm. Based on randomized krasnosel'skii mann iterations and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithms.