New inertial proximal gradient methods for unconstrained convex optimization problems

The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algo...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 18
Main Authors: Duan, Peichao, Zhang, Yiqun, Bu, Qinxiong
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.12.2020
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Alternated inertial acceleration
Analysis
Applications of Mathematics
Computational geometry
Convergence
Convex analysis
Convex optimization
Convexity
Inertial acceleration
Mathematics
Mathematics and Statistics
Optimization
Proximal operator
Viscosity approximation
47H10
Alternated inertial acceleration
Inertial acceleration
Convex optimization
90C25
47H09
65K10
Proximal operator
47J25
Viscosity approximation
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:The proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02522-6