  Nesterov's accelerated gradient (AG) is a popular technique to optimize
objective functions comprising two components: a convex loss and a penalty
function. While AG methods perform well for convex penalties, such as the
LASSO, convergence issues may arise when it is applied to nonconvex penalties,
such as SCAD. A recent proposal generalizes Nesterov's AG method to the
nonconvex setting. The proposed algorithm requires specification of several
hyperparameters for its practical application. Aside from some general
conditions, there is no explicit rule for selecting the hyperparameters, and
how different selection can affect convergence of the algorithm. In this
article, we propose a hyperparameter setting based on the complexity upper
bound to accelerate convergence, and consider the application of this nonconvex
AG algorithm to high-dimensional linear and logistic sparse learning problems.
We further establish the rate of convergence and present a simple and useful
bound to characterize our proposed optimal damping sequence. Simulation studies
show that convergence can be made, on average, considerably faster than that of
the conventional proximal gradient algorithm. Our experiments also show that
the proposed method generally outperforms the current state-of-the-art methods
in terms of signal recovery.
