An Inertial Semi-forward-reflected-backward Splitting and Its Application

Inertial methods play a vital role in accelerating the convergence speed of optimization algorithms. This work is concerned with an inertial semi-forward-reflected-backward splitting algorithm of approaching the solution of sum of a maximally monotone operator, a cocoercive operator and a monotone-L...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series Vol. 38; no. 2; pp. 443 - 464
Main Authors: Zong, Chun Xiang, Tang, Yu Chao, Zhang, Guo Feng
Format: Journal Article
Language:English
Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.02.2022
Springer Nature B.V
Subjects:
Algorithms
Computational geometry
Convergence
Iterative algorithms
Mathematics
Mathematics and Statistics
Operators (mathematics)
Optimization
Splitting
composite monotone inclusions
65K05
composite convex optimization
90C25
Operator splitting
total variation
47H05
inertial scheme
ISSN:1439-8516, 1439-7617
Online Access:Get full text
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Summary:Inertial methods play a vital role in accelerating the convergence speed of optimization algorithms. This work is concerned with an inertial semi-forward-reflected-backward splitting algorithm of approaching the solution of sum of a maximally monotone operator, a cocoercive operator and a monotone-Lipschitz continuous operator. The theoretical convergence properties of the proposed iterative algorithm are also presented under mild conditions. More importantly, we use an adaptive stepsize rule in our algorithm to avoid calculating Lipschitz constant, which is generally unknown or difficult to estimate in practical applications. In addition, a large class of composite monotone inclusion problem involving mixtures of linearly composed and parallel-sum type monotone operators is solved by combining the primal-dual approach and our proposed algorithm. As a direct application, the obtained inertial algorithm is exploited to composite convex optimization problem and some numerical experiments on image deblurring problem are also investigated to demonstrate the efficiency of the proposed algorithm.
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-022-0649-x