Метод операторної екстраполяції для варіаційних нерівностей в банахових просторах
The paper presents new algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflected-backward algorithm, which uses the Alber generalized projection instead of the metric one. The second alg...
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| Date: | 2023 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
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| Subjects: | |
| Online Access: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/317 |
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| Journal Title: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Summary: | The paper presents new algorithms for solving variational inequalities in uniformly convex Banach spaces. The first algorithm is a modification of the forward-reflected-backward algorithm, which uses the Alber generalized projection instead of the metric one. The second algorithm is an adaptive version of the first one, where the monotone step size update rule is used, which does not require knowledge of Lipschitz constants and linear search procedure. Theorems on the weak convergence of methods are proved. Also, for the first algorithm, an efficiency estimate is proved. |
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