A Constrained Linearly Involved Generalized Moreau Enhanced Model and Its Proximal Splitting Algorithm

Abstract

In this paper, we propose a constrained LiGME (cLiGME) model by incorporating newly multiple convex constraints into the LiGME (Linearly involved Generalized Moreau Enhanced) model which was established recently for many scenarios in sparsity-rank-aware least squares estimation. The cLiGME model can exploit flexibly a priori knowledge on the target to be estimated while keeping the advantage of the LiGME model, i.e., mathematically sound mechanism for nonconvex enhancements of linearly involved convex regularizers. For the cLiGME model, we present a new proximal splitting type algorithm of guaranteed convergence to a global minimizer and demonstrate its effectiveness with a simple numerical experiment.