Bregman iterative regularization using model functions for nonconvex nonsmooth optimization

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