A hybrid splitting method for smoothing Tikhonov regularization problem

Journal of Inequalities and Applications

卷:2016

Zheng Peng¹  Yu-Hua Zeng²  Yu-Fei Yang² 

[1] College of Mathematics and Computer Science, Fuzhou University;

[2] College of Mathematics and Econometrics, Hunan University;

关键词: Tikhonov regularization;    augmented Lagrangian method;    parallel splitting method;    alternative direction method of multipliers;   

DOI  :  10.1186/s13660-016-0981-8

来源: DOAJ

【 摘 要 】

Abstract In this paper, a hybrid splitting method is proposed for solving a smoothing Tikhonov regularization problem. At each iteration, the proposed method solves three subproblems. First of all, two subproblems are solved in a parallel fashion, and the multiplier associated to these two block variables is updated in a rapid sequence. Then the third subproblem is solved in the sense of an alternative fashion with the former two subproblems. Finally, the multiplier associated to the last two block variables is updated. Global convergence of the proposed method is proven under some suitable conditions. Some numerical experiments on the discrete ill-posed problems (DIPPs) show the validity and efficiency of the proposed hybrid splitting method.

【 授权许可】

Unknown