Perturbation resilience of proximal gradient algorithm for composite objectives


Authors

Yanni Guo - College of Science, Civil Aviation University of China, Tianjin, 300300, P. R. China. Wei Cui - College of Science, Civil Aviation University of China, Tianjin, 300300, P. R. China. Yansha Guo - School of Information Technology Engineering, Tianjin University of Technology and Education, Tianjin, 300222, P. R. China.


Abstract

In this paper, we study the perturbation resilience of a proximal gradient algorithm under the general Hilbert space setting. With the assumption that the error sequence is summable, we prove that the iterative sequence converges weakly to a solution of the composite optimization problem. We also show the bounded perturbation resilience of this iterative method and apply it to the lasso problem.


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ISRP Style

Yanni Guo, Wei Cui, Yansha Guo, Perturbation resilience of proximal gradient algorithm for composite objectives, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5566--5575

AMA Style

Guo Yanni, Cui Wei, Guo Yansha, Perturbation resilience of proximal gradient algorithm for composite objectives. J. Nonlinear Sci. Appl. (2017); 10(10):5566--5575

Chicago/Turabian Style

Guo, Yanni, Cui, Wei, Guo, Yansha. "Perturbation resilience of proximal gradient algorithm for composite objectives." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5566--5575


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