Imposing Early and Asymptotic Constraints on Ligme with Application to Nonconvex Enhancement of Fused Lasso Models

Abstract

For the constrained LiGME model, a nonconvexly regularized least squares estimation model, under its overall convexity condition, we newly 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 constraint, requires the limit of estimation sequence to achieve the corresponding condition. The second type constraint, called the early constraint, requires every vector in estimation sequence to achieve the corresponding condition. We also propose nonconvex and robustness enhancements of fused lasso models for sparse piecewise constant signal estimations, possibly under nonzero baseline assumptions, to which the proposed enhancements with two types of constraints can achieve robustness against possible model mismatch as well as higher estimation accuracy compared with conventional fused lasso models.