Imposing early and asymptotic constraints on LiGME with application to bivariate nonconvex enhancement of fused lasso models

TL;DR

This paper introduces an iterative algorithm for the LiGME model that guarantees convergence to the global optimum while handling multiple constraints, and applies it to enhance fused lasso models for sparse signal estimation.

Contribution

It presents a novel algorithm for constrained LiGME models with proven convergence and extends it to a bivariate nonconvex fused lasso enhancement for improved sparse signal estimation.

Findings

Algorithm guarantees convergence to global optimum.

Effective handling of multiple constraints simultaneously.

Improved sparse piecewise constant signal estimation.

Abstract

For the constrained LiGME model, a nonconvexly regularized least squares estimation model, we present an iterative algorithm of guaranteed convergence to its globally optimal solution. The proposed algorithm can deal with two different types of constraints simultaneously. The first type constraint, called the asymptotic one, requires the limit of estimation sequence to achieve the corresponding condition. The second type constraint, called the early one, requires every vector in estimation sequence to achieve the condition. We also propose a bivariate nonconvex enhancement of fused lasso models with effective constraint for sparse piecewise constant signal estimations. (This is an improved version of [Yata and Yamada, ICASSP 2024].)