Abstract
In this paper, we introduce inertial Tseng’s extragradient algorithms combined with normal-S iteration process for solving variational inequality problems involving pseudo-monotone and Lipschitz continuous operators. Under mild conditions, we establish the weak convergence results in Hilbert spaces. Numerical examples are also presented to show that faster behaviour of the proposed method.
Highlights
Variational inequality problems are extremely powerful tools to study the many nonlinear problems arising in several branches of applied science in different framework due to its successful applications in fields including control theory, game theory, transportation science, economic equilibrium and engineering sciences
It is worth mentioning that the variational inequality problem is a central problem in optimization theory
We focus on projection methods for solving the variational inequality problems, introduced by Goldstein [10] and defined by x1 ∈ C, xn = PC for all n ∈ N, (1.2)
Summary
Variational inequality problems are extremely powerful tools to study the many nonlinear problems arising in several branches of applied science in different framework due to its successful applications in fields including control theory, game theory, transportation science, economic equilibrium and engineering sciences. Authors in [12,17,18,19,22] studied the convergence behaviour of projection methods and its variants for strongly pseudo-monotone and Lipschitzian variational inequality problems. The weak convergence of Tseng’s extragradient method for solving monotone Lipschitz continuous variational inequalities was established in [36], with a different choice of parameters, Thong and Hieu [34] established the strong convergence results for strongly pseudomonotone variational inequalities. In this article, motivated by the work of Tseng’s [36] and Sahu [24], we consider the variational inequality problem in Hilbert spaces and proposed an inertial normal S-type Tseng’s extragradient Algorithm for solution of variational inequality problems.
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