LAUSR

The variational inequality problem plays an important role in nonlinear analysis and optimization. It is a generalization of the nonlinear complementarity problem. For a variational inequality problem in a Hilbert space, the extragradient algorithm with inertial effects has been studied. For a variational inequality problem in a Banach space, Nakajo introduced Haugazeau's hybrid method and Liu introduced the Halpern subgradient extragradient method. In this paper, we construct a new inertial iterative method for solving variational inequality problems in Banach spaces based on the work we mentioned above. We propose a strong convergence theorem. As applications, our result can be used to solve constrained convex minimization problems.