Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems

In this paper, two new algorithms are introduced for solving a pseudomontone variational inequality problem with a Lipschitz condition in a Hilbert space. The algorithms are constructed around three methods: the subgradient extragradient method, the inertial method and the viscosity method. With a new stepsize rule is incorporated, the algorithms work without any information of Lipschitz constant of operator. The weak convergence of the first algorithm is established, while the second one is strongly convergent which comes from the viscosity method. In order to show the computational effectiveness of our algorithms, some numerical results are provided.