Global convergence of block Bregman proximal iteratively reweighted algorithm with extrapolation

In this paper, we propose a Bregman 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 separable structure. The proposed algorithm can be used to solve the \(\ell _p(0<p<1)\) ${\ell }_p(0<p<1)$ regularization problem by employing an update strategy of the smoothing parameter in its smooth approximation model. When the extrapolation parameter satisfies certain conditions, 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 superiority of the proposed algorithm.