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

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...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2018; no. 1; pp. 103 - 15
Main Authors: Guo, Yanni, Cui, Wei
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 2018
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Analysis
Applications of Mathematics
Bounded perturbation resilience
Convergence
Convex minimization problem
Hilbert space
Mathematics
Mathematics and Statistics
Modified proximal gradient algorithm
Optimization
Perturbation
Resilience
Strong convergence
Viscosity approximation
Modified proximal gradient algorithm
Strong convergence
Bounded perturbation resilience
Convex minimization problem
Viscosity approximation
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary: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.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1695-x