AUTHOR=Yang Haoxing , Zhang Hui , Wang Hongxia , Cheng Lizhi 

TITLE=Bregman iterative regularization using model functions for nonconvex nonsmooth optimization

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 8 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.1031039

DOI=10.3389/fams.2022.1031039

ISSN=2297-4687

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 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-{\L}ojasiewicz 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.