A double iteratively reweighted algorithm for solving group sparse nonconvex optimization models

TL;DR

This paper introduces a novel double iteratively reweighted algorithm for efficiently solving nonconvex, nonsmooth group sparse optimization problems with convergence guarantees and practical effectiveness demonstrated through preliminary experiments.

Contribution

It proposes a new double reweighted algorithm for nonconvex group sparse models, extending its application to constrained problems with convergence analysis.

Findings

Guarantees feasibility of each iteration

Proves cluster point is a stationary point

Demonstrates efficiency in preliminary tests

Abstract

In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse structures. At each iteration, we combine convex surrogate with first-order information to construct linearly constrained subproblems to handle the concavity of model. The corresponding subproblems are then solved by alternating direction method of multipliers to satisfy the specific stop criteria. In particular, under mild assumptions, we prove that our algorithm guarantees the feasibility of each subsequent iteration point, and the cluster point of the resulting feasible sequence is shown to be a stationary point. Additionally, we extend the group sparse optimization model, pioneer the application of the double iterative reweighted algorithm to solve constrained group sparse models (which exhibits superior efficiency), and incorporate a generalized Bregman distance to characterize the algorithm's termination conditions. Preliminary numerical experiments show the efficiency of the proposed method.