Before revision:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging , that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information on the interface of these subdomains,thus leading to highly parallel algorithms with good load balance.
After revision:  In this paper, we propose the overlapping Domain Decomposition Methods(DDMs) to solve the nonconvex optimization problem in ptychographic imaging , that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information in the overlapping regions of these subdomains,thus leading to highly parallel algorithms with good load balance.