Bregman iterative regularization using model functions for nonconvex nonsmooth optimization

Abstract

In this paper, we propose a new algorithm called ModelBI by blending the Bregman iterative regularization method and the model function technique for solving a class of nonconvex nonsmooth optimization problems. On one hand, we use the model function technique, which is essentially a first-order approximation to the objective function, to go beyond the traditional Lipschitz gradient continuity. On the other hand, we use the Bregman iterative regularization to generate solutions fitting certain structures. Theoretically, we show the global convergence of the proposed algorithm with the help of the Kurdyka-Łojasiewicz property. Finally, we consider two kinds of nonsmooth phase retrieval problems and propose an explicit iteration scheme. Numerical results verify the global convergence and illustrate the potential of our proposed algorithm.