A Convexly Constrained LiGME Model and Its Proximal Splitting Algorithm

TL;DR

This paper introduces a convexly constrained LiGME model that incorporates multiple convex constraints for improved sparsity-rank-aware estimation, along with a proximal splitting algorithm, validated through signal processing experiments.

Contribution

It extends the LiGME model by integrating multiple convex constraints and develops a proximal splitting algorithm for efficient optimization.

Findings

The cLiGME model effectively incorporates multiple convex constraints.

The proposed algorithm demonstrates good convergence properties.

Numerical experiments show improved performance in signal processing tasks.

Abstract

For the sparsity-rank-aware least squares estimations, the LiGME (Linearly involved Generalized Moreau Enhanced) model was established recently in [Abe, Yamagishi, Yamada, 2020] to use certain nonconvex enhancements of linearly involved convex regularizers without losing their overall convexities. In this paper, for further advancement of the LiGME model by incorporating multiple a priori knowledge as hard convex constraints, we newly propose a convexly constrained LiGME (cLiGME) model. The cLiGME model can utilize multiple convex constraints while preserving benefits achieved by the LiGME model. We also present a proximal splitting type algorithm for the proposed cLiGME model. Numerical experiments demonstrate the efficacy of the proposed model and the proposed optimization algorithm in a scenario of signal processing application.