Split variational inequality problem

This paper proposes a new algorithm for solving the split variational inequality problem in Hilbert spaces. In order to solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Compared with the work by Censor et al. (Numer. Algor., 59:301-323, 2012), the new algorithm gives strong convergence results. It shows that the iterative method converges strongly under weaker assumptions than the ones used recently. Some numerical examples are also given to illustrate the convergence analysis of the considered algorithm.

8p nhanchienthien 25-07-2023 5 4   Download

In this paper, we introduce two different interative methods for finding a solution of a split pseudomonotone variational inequality and a split feasibility problem in Hilbert spaces. The proposed algorithm is generated based on the subgradient extragradient method which requires only two projections at each iteration step and the second projection is conducted onto the half-space containing the constrained set.

9p viharry 15-12-2022 8 2   Download

The split variational inequality problem (SVIP) was first introduced by Censor et al. Up to now, there is a long list of works concerning algorithms to solve (SVIP). In this paper, we study the split variational inequality problem in Hilbert spaces. In order to solve this problem, we propose a self-adaptive algorithm.

9p viirenerosenfeld 02-06-2022 13 1   Download

In this paper, we propose an iterative method for approximating the solution of the bilevel problem. This method bases on the result presented by Tran Viet Anh and Le Dung Muu in 2016, which is a combination between the projection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. The strong convergence of the method is proven. We close the paper by considering an example to illustrate the strong convergence of method.

10p nguaconbaynhay12 13-06-2021 26 1   Download