Two Algorithms For Variational Inequality Problems

In this paper,firstly,the existence and uniqueness of the solution of quasi variational inequality(QVI)in Hilbert space are studied.Secondly,the convergence of the approach point algorithm for solving variational inequalities is studied.Firstly,based on the inertial algorithm and projection compression algorithm,an improved interval projection compression algorithm for solving quasi variational inequality is proposed.The convergence of the algorithm is proved in Hilbert space.In the numerical result part,the effectiveness of the algorithm is verified by numerical examples.Secondly,we study the convergence of the approach point algorithm of the variational inequality.Under the assumption of Lipschitz continuity,we prove that the dynamic system of the strongly pseudomonotone variational inequality has a unique equilibrium solution.In addition,the solution is globally exponentially stable.The effectiveness of the theoretical results is analyzed with an example,and numerical simulation is carried out with MATLAB.The numerical results show that,the global exponential trajectory of the dynamical system converges to the unique solution of the variational inequality.