Weak and Strong Convergence of Self Adaptive Inertial Subgradient Extragradient Algorithms for Solving Variational Inequality Problems

Many solutions of variational inequalities have been proposed, among which the subgradient extragradient method has obvious advantages. Two different algorithms are given for solving variational inequality problem in this paper. The problem we study is defined in a real Hilbert space and has L-Lipschitz and pseudomonotone condition. Two new algorithms adopt inertial technology and non-monotonic step size rule, and their convergence can still be proved when the value of L is not given in advance.Finally, some numerical results are designed to demonstrate the computational efficiency of our two new algorithms.