期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 55, 期 4, 页码 1549-1577出版社
SIAM PUBLICATIONS
DOI: 10.1137/16M1078604
关键词
Douglas-Rachford splitting method; weakly convex penalty; Fejer monotone; convergence; convergence rate; rate of asymptotic regularity
资金
- PAPD of Jiangsu Higher Education Institutions
- Natural Science Foundation of China [11371015, 11625105, 11371197, 11431002]
- Hong Kong Research Grants Council [12313516]
We consider the convergence of the Douglas-Rachford splitting method (DRSM) for minimizing the sum of a strongly convex function and a weakly convex function; this setting has various applications, especially in some sparsity-driven scenarios with the purpose of avoiding biased estimates which usually occur when convex penalties are used. Though the convergence of the DRSM has been well studied for the case where both functions are convex, its results for some nonconvexfunction- involved cases, including the strongly + weakly convex case, are still in their infancy. In this paper, we prove the convergence of the DRSM for the strongly + weakly convex setting under relatively mild assumptions compared with some existing work in the literature. Moreover, we establish the rate of asymptotic regularity and the local linear convergence rate in the asymptotical sense under some regularity conditions.
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