Modified Subgradient Extragradient Method for Variational Inequality Problems and Fixed Point Problems

Many approaches inquiring into variational inequality problems have been put forward, among which subgradient extragradient method is of great significance. A novel algorithm is presented in this article for resolving quasi-nonexpansive fixed point problem and pseudomonotone variational inequality problem in a real Hilbert interspace. In order to decrease the execution time and quicken the velocity of convergence, the proposed algorithm adopts an inertial technology. Moreover, the algorithm is by virtue of a non-monotonic step size rule to acquire strong convergence theorem without estimating the value of Lipschitz constant. Finally, numerical results on some problems authenticate that the algorithm has preferable efficiency than other algorithms.