Modified Extragradient Methods with Inertial Technique for Solving Pseudo-Monotone Variational Inequality Problems.

In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive Banach spaces. Under some reasonable assumptions on the parameters, strong convergence and R-linear convergence results for our methods are established without prior knowledge of the Lipschitz constant of the bounded operator. Moreover, we provide some numerical experiments to demonstrate the efficiency of our proposed algorithm, and numerical results reveal that our algorithm outruns other algorithms in the literature. [ABSTRACT FROM AUTHOR]