An accelerated viscosity forward-backward splitting algorithm with the linesearch process for convex minimization problems

In this paper, we consider and investigate a convex minimization problem of the sum of two convex functions in a Hilbert space. The forward-backward splitting algorithm is one of the popular optimization methods for approximating a minimizer of the function; however, the stepsize of this algorithm d...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2021; no. 1; pp. 1 - 19
Main Authors: Suantai, Suthep, Jailoka, Pachara, Hanjing, Adisak
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 27.02.2021
Springer Nature B.V
SpringerOpen
Subjects:
Algorithms
Analysis
Applications of Mathematics
Approximation
Convex minimization problems
Forward-backward splitting
Hilbert space
Inertial techniques
Linesearch
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
Signal reconstruction
Splitting
Strong convergence
Viscosity
Viscosity approximation
Strong convergence
65K05
90C30
Inertial techniques
90C25
Forward-backward splitting
Convex minimization problems
Linesearch
Viscosity approximation
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper, we consider and investigate a convex minimization problem of the sum of two convex functions in a Hilbert space. The forward-backward splitting algorithm is one of the popular optimization methods for approximating a minimizer of the function; however, the stepsize of this algorithm depends on the Lipschitz constant of the gradient of the function, which is not an easy work to find in general practice. By using a new modification of the linesearches of Cruz and Nghia [Optim. Methods Softw. 31:1209–1238, 2016 ] and Kankam et al. [Math. Methods Appl. Sci. 42:1352–1362, 2019 ] and an inertial technique, we introduce an accelerated viscosity-type algorithm without any Lipschitz continuity assumption on the gradient. A strong convergence result of the proposed algorithm is established under some control conditions. As applications, we apply our algorithm to solving image and signal recovery problems. Numerical experiments show that our method has a higher efficiency than the well-known methods in the literature.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02571-5