A stochastic coordinate descent primal-dual algorithm with dynamic stepsize for large-scale composite optimization

TL;DR

This paper introduces a stochastic coordinate descent primal-dual algorithm with dynamic stepsize for large-scale composite convex optimization, ensuring convergence through randomized iterations and nonexpansive operator properties.

Contribution

It presents a novel stochastic coordinate descent primal-dual splitting algorithm with dynamic stepsize, extending coordinate descent methods to complex convex optimization problems.

Findings

Algorithm converges under specified conditions

Applicable to large-scale composite convex problems

Demonstrated effectiveness through two applications

Abstract

In this paper 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. With the idea of coordinate descent, we design a stochastic coordinate descent primal-dual splitting algorithm with dynamic stepsize. Based on randomized Modified Krasnosel'skii-Mann iterations and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithms. Moreover, we give two applications of our method.