Метод операторної екстраполяції для варіаційних  нерівностей в банахових просторах

Volodymyr Semenov; Oleh Kharkov

Volodymyr Semenov д. ф.-м. н., професор, Київський національний університет імені Тараса Шевченка, вул. Володимирська, 64/13, 01601, Київ
Oleh Kharkov аспірант, Київський національний університет імені Тараса Шевченка, вул. Володимирська, 64/13, 01601, Київ

Abstract

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.

References

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Operator extrapolation method for variational inequalities in Banach spaces

Abstract

References