Strong convergence and bounded perturbation resilience of a modified proximal gradient algorithm

Journal of Inequalities and Applications

Yanni Guo¹  Wei Cui¹ 

[1] College of Science, Civil Aviation University of China;

关键词: Strong convergence;    Bounded perturbation resilience;    Modified proximal gradient algorithm;    Viscosity approximation;    Convex minimization problem;   

DOI  :  10.1186/s13660-018-1695-x

来源: DOAJ

【 摘 要 】

Abstract The proximal gradient algorithm is an appealing approach in finding solutions of non-smooth composite optimization problems, which may only has weak convergence in the infinite-dimensional setting. In this paper, we introduce a modified proximal gradient algorithm with outer perturbations in Hilbert space and prove that the algorithm converges strongly to a solution of the composite optimization problem. We also discuss the bounded perturbation resilience of the basic algorithm of this iterative scheme and illustrate it with an application.

【 授权许可】

Unknown