  In this paper, we propose a novel adaptive sieving (AS) technique and an
enhanced AS (EAS) technique, which are solver independent and could accelerate
optimization algorithms for solving large scale convex optimization problems
with intrinsic structured sparsity. We establish the finite convergence
property of the AS technique and the EAS technique with inexact solutions of
the reduced subproblems. As an important application, we apply the AS technique
and the EAS technique on the convex clustering model, which could accelerate
the state-of-the-art algorithm SSNAL by more than 7 times and the algorithm
ADMM by more than 14 times.
