  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.
