Global convergence of block proximal iteratively reweighted algorithm with extrapolation

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-Łojasiewicz (KL) property on the objective function. Numerical experiments are given to indicate the efficiency of the proposed algorithm.