A hybrid splitting method for smoothing Tikhonov regularization problem
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- 作者：Yu-Hua Zeng ; Zheng Peng ; Yu-Fei Yang
- 关键词：Tikhonov regularization ; augmented Lagrangian method ; parallel splitting method ; alternative direction method of multipliers
- 刊名：Journal of Inequalities and Applications
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：2016
- 期：1
- 全文大小：1,559 KB
- 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1029-242X
文摘
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.