  Nonconvex optimization problems arise in different research fields and arouse
lots of attention in signal processing, statistics and machine learning. In
this work, we explore the accelerated proximal gradient method and some of its
variants which have been shown to converge under nonconvex context recently. We
show that a novel variant proposed here, which exploits adaptive momentum and
block coordinate update with specific update rules, further improves the
performance of a broad class of nonconvex problems. In applications to sparse
linear regression with regularizations like Lasso, grouped Lasso, capped
$\ell_1$ and SCAP, the proposed scheme enjoys provable local linear
convergence, with experimental justification.
