A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank Minimization

TL;DR

This paper introduces a convergent parallel best-response algorithm with exact line search for nonconvex sparsity-regularized rank minimization, achieving faster convergence and guaranteed stationary point convergence compared to existing methods.

Contribution

It presents a novel parallel best-response algorithm with an efficient exact line search for nonconvex rank minimization, improving convergence speed and reliability.

Findings

Faster convergence than subgradient and block coordinate descent algorithms.

Guaranteed convergence to a stationary point.

Efficient closed-form exact line search implementation.

Abstract

In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand, its convergence to a stationary point is guaranteed, while ADMM algorithms only converge for convex problems. Furthermore, the exact line search procedure in the proposed algorithm is performed efficiently in closed-form to avoid the meticulous choice of stepsizes, which is however a common bottleneck in subgradient algorithms and successive convex approximation algorithms. Finally, the proposed algorithm is numerically tested.