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Convergence of multi-block Bregman ADMM for nonconvex composite problems

Science China(Information Sciences) 2018年第12期61卷 53-64页

作者： Fenghui WANG Wenfei CAO Zongben XU School of Mathematics and Statistics Xi'an Jiaotong University Department of Mathematics Luoyang Normal University School of Mathematics and Information Science Shaanxi Normal University

The alternating direction method with multipliers(ADMM) is one of the most powerful and successful methods for solving various composite problems. The convergence of the conventional ADMM(i.e.,2-block) for convex objective functions has been stated for a long time, and its convergence for nonconvex objective functions has, however, been established very recently. The multi-block ADMM, a natural extension of ADMM, is a widely used scheme and has also been found very useful in solving various nonconvex optimization problems. It is thus expected to establish the convergence of the multi-block ADMM under nonconvex frameworks. In this paper, we first justify the convergence of 3-block Bregman ADMM. We next extend these results to the N-block case(N≥3), which underlines the feasibility of multi-block ADMM applications in nonconvex settings. Finally, we present a simulation study and a real-world application to support the correctness of the obtained theoretical assertions.

关键词： nonconvex regularization alternating direction method subanalytic function K-L inequality Bregman distance

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SPARSE RECOVERY BASED ON THE GENERALIZED ERROR FUNCTION

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Journal of Computational Mathematics 2024年第3期42卷 679-704页

作者： Zhiyong Zhou Department of Statistics and Data Science and Institute of Digital FinanceHangzhou City UniversityHangzhou 310015China

In this paper,we offer a new sparse recovery strategy based on the generalized error *** introduced penalty function involves both the shape and the scale parameters,making it extremely *** both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are *** practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are *** experiments are carried out to demonstrate the benefits of the suggested approach in a variety of *** practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.

关键词： Sparse recovery Generalized error function nonconvex regularization Itera-tive reweighted Li Difference of convex functions algorithms

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