Modified inertial subgradient projection and contraction method for solving nonmonotone variational inequality problem in Hilbert space

Abstract

In almost all existing projection and contraction methods including their modifications, the range of the constant is (0, 2) and has the similar definitions. In this paper, we introduce a new inertial subgradient projection and contraction method for solving a variational inequality problem in Hilbert space. In our method, the mapping is not required to be pseudomonotone, the range of is relaxed from (0, 2) to , is computed by a new manner and the self-adaptive step size admitted to be increasing is used for dealing with the unknown Lipschitz constant. Under some new conditions, we prove the strong convergence of the proposed method. Some numerical examples and an application are presented to illustrate the effectiveness of our method and compare the numerical results with some related methods in the literature.