A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programmingReportar como inadecuado




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Journal of Inequalities and Applications

, 2017:129

First Online: 05 June 2017Received: 22 January 2017Accepted: 10 May 2017DOI: 10.1186-s13660-017-1405-0

Cite this article as: Liu, J., Duan, Y. & Sun, M. J Inequal Appl 2017 2017: 129. doi:10.1186-s13660-017-1405-0

Abstract

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers ADMM, and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval \1,+\infty\. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case \\mathcal{O}1-k\ convergence rate in both the ergodic and the non-ergodic senses, where k denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.

Keywordsalternating direction method of multipliers convex programming mixed variational inequalities compressed sensing MSC90C25 90C30 



Autor: Jing Liu - Yongrui Duan - Min Sun

Fuente: https://link.springer.com/







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