On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications

This paper presents several modified subgradient extragradient methods with inertial effects to approximate solutions of variational inequality problems in real Hilbert spaces. The operators involved are either pseudomonotone Lipschitz continuous or pseudomonotone non-Lipschitz continuous. The advantage of the suggested algorithms is that they can work adaptively without the prior information of the Lipschitz constant of the mapping involved. Strong convergence theorems of the proposed algorithms are established under some suitable conditions. Finally, some numerical experiments are given to verify the advantages and efficiency of the proposed iterative algorithms with respect to previously known ones.