Three-operator splitting algorithm for a class of variational inclusion problems

This paper concerns with a new three-operator splitting algorithm for solving a class of variational inclusions. The main advantage of the proposed algorithm is that it can be easily implemented without the prior knowledge of Lipschitz constant, strongly monotone constant and cocoercive constant of...

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Vydáno v:Bulletin of the Iranian Mathematical Society Ročník 46; číslo 4; s. 1055 - 1071
Hlavní autoři: Van Hieu, Dang, Van Vy, Le, Quy, Pham Kim
Médium: Journal Article
Jazyk:angličtina
Vydáno: Singapore Springer Singapore 01.08.2020
Témata:
Mathematics
Mathematics and Statistics
Original Paper
47J20
Tseng’s method
Forward–backward method
Operator splitting method
47H05
47J25
65J15
91B50
ISSN:1017-060X, 1735-8515
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Popis
Shrnutí:This paper concerns with a new three-operator splitting algorithm for solving a class of variational inclusions. The main advantage of the proposed algorithm is that it can be easily implemented without the prior knowledge of Lipschitz constant, strongly monotone constant and cocoercive constant of component operators. A reason explained for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. The strong convergence of the algorithm is established. Several fundamental numerical experiments are given to illustrate the behavior of the new algorithm and compare it with other algorithms.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-019-00312-5