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For the constrained LiGME model, a nonconvexly regularized least squaresestimation model, under its overall convexity condition, we newly present aniterative algorithm of guaranteed convergence to its globally optimal solution.The proposed algorithm can deal with two different types of constraintssimultaneously. The first type called the asymptotic constraint requires forthe limit point of the produced sequence by the proposed algorithm to achieveasymptotically. The second type called the early constraint requires for thewhole sequence by the proposed algorithm to satisfy. We also propose anonconvex and constraint enhancement of fused lasso models for sparse piecewiseconstant signal estimations, possibly under nonzero baseline assumptions, towhich the proposed enhancement with two types of constraints can achieverobustness against possible model mismatch as well as higher estimationaccuracy compared with conventional fused lasso type models.

Imposing early and asymptotic constraints on LiGME with application to nonconvex enhancement of fused lasso models