  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].)
