An active set Barzilar–Borwein algorithm for $$l_{0}$$ regularized optimization

Abstract

In this paper, we develop an active set identification technique for the $$\ell _0$$ regularization optimization. Such a technique has a strong ability to identify the zero components in a neighbourhood of a strict L-stationary point. Based on the identification technique, we propose an active set Barzilar–Borwein algorithm and prove that any limit point of the sequence generated by the algorithm is a strong stationary point. Some preliminary numerical results are provided, showing that the method is promising.