Trust-Region Methods for Sparse Relaxation

TL;DR

This paper introduces a trust-region optimization method for sparse recovery that leverages past gradients for better Hessian approximation, leading to more accurate solutions and faster convergence.

Contribution

It presents a novel trust-region approach utilizing historical gradients for improved sparse recovery, outperforming gradient projection methods.

Findings

Reduces spurious solutions effectively

Improves computational convergence time

Outperforms gradient projection methods

Abstract

In this paper, we solve the l2-l1 sparse recovery problem by transforming the objective function of this problem into an unconstrained differentiable function and apply a limited-memory trust-region method. Unlike gradient projection-type methods, which uses only the current gradient, our approach uses gradients from previous iterations to obtain a more accurate Hessian approximation. Numerical experiments show that our proposed approach eliminates spurious solutions more effectively while improving the computational time to converge.