  In this paper, we propose a proximal iteratively reweighted algorithm with
extrapolation based on block coordinate update aimed at solving a class of
optimization problems which is the sum of a smooth possibly nonconvex loss
function and a general nonconvex regularizer with a special structure. The
proposed algorithm can be used to solve the $\ell_p(0<p<1)$ regularization
problem by employing a updating strategy of the smoothing parameter. It is
proved that there exists the nonzero extrapolation parameter such that the
objective function is nonincreasing. Moreover, the global convergence and local
convergence rate are obtained by using the Kurdyka-{\L}ojasiewicz (KL) property
on the objective function. Numerical experiments are given to indicate the
efficiency of the proposed algorithm.
