Bregman iterative regularization using model functions for nonconvex nonsmooth optimization - Yang, Haoxing; Zhang, Hui; Wang, Hongxia; Cheng, Lizhi (Frontiers in Applied Mathematics and Statistics, 2022)
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 continuity; On the other hand, we use the Bregman iterative regularization to generate solutions fitting certain structure. Theoretically, we show the global convergence of the proposed algorithm with the help of Kurdyka-Łojasiewicz property. At last, we consider two class of nonsmooth phase retrieval problems and propose a kind of explicit iteration steps. Numerical results verify the global convergence and illustrate the potential of our proposed algorithm.