An Adaptive Inertial Projection And Contraction Algorithm For Solving Variational Inequalities

Variational inequality provides a unified and general framework for a wide class of problems arising from mathematics,management science,economics and some other research fields.Variational inequality is a description of the problem,which occupies an important position in mathematical programming and has a close rela-tionship with optimization.With the era of big data coming,it is very necessary and urgent to design some fast numerical algorithms for these problems,which is of great practical significance.In this paper,we mainly study a self-adaptive inertial projection and contrac-tion algorithm for variational inequality.Firstly,we propose a self-adaptive inertial projection and contraction algorithm for the variational inequality in a Hilbert space H.Under assumption that the operator f is continuous and monotone,we prove the weak convergence of the algorithm.Compared with the inertial projection and contraction algorithm which needs f to be Lipschitz continuous and monotone,our assumption is much weaker.In addition,the range of parameters has been improved by a detailed analysis.Finally,we report some preliminary computational results to show the efficiency and advantages of the algorithm.