A parameterized Douglas-Rachford Splitting algorithm for nonconvex optimization

TL;DR

This paper introduces a parameterized Douglas-Rachford splitting algorithm tailored for nonconvex optimization problems, demonstrating its convergence and effectiveness in data science applications like sparse least squares, feasibility, and low-rank matrix completion.

Contribution

The paper develops a new parameterized Douglas-Rachford splitting method with a novel merit function for nonconvex problems, and validates its performance on key data science tasks.

Findings

Convergence of the entire sequence is established using a new merit function.

Numerical experiments show superior performance over classical methods.

Effective in solving sparsity, feasibility, and low-rank matrix problems.

Abstract

In this paper, we study a parameterized Douglas-Rachford splitting method for a class of nonconvex optimization problem. A new merit function is constructed to establish the convergence of the whole sequence generated by the parameterized Douglas-Rachford splitting method. We then apply the parameterized Douglas-Rachford splitting method to three important classes of nonconvex optimization problems arising in data science: sparsity constrained least squares problem, feasibility problem and low rank matrix completion. Numerical results validate the effectiveness of the parameterized Douglas-Rachford splitting method compared with some other classical methods.