A Smoothing Inexact Newton Method For Variational Inequality

Variational inequality problem is a very important research direction in the field of applied mathematics, many optimization problems can be converted to be solved by variational inequality problems. Research algorithm on variational inequality problem have important theoretical significance and practical value. The main research work includes the following two aspects:First of all, the use of smooth function to smooth of variational inequality problem, give improved smoothing Newton algorithm for solving variational inequality, algorithm of the initial point without restrictions, each iteration solving a system of linear equations, performs a line search, in the process of using iterative smoothing Newton method is used to solve, combined with variable neighborhood search algorithm is global convergence is good and accurate, and then search the whole area, to find the global optimal solution. Numerical experiments show that the improved algorithm has better convergence and search precision. Secondly, based on the ideas of the smoothing Newton method, in view of the smooth algorithm to solve the linear problem of low efficiency of exact solutions of defects, and puts forward the solving variational inequality problems of smooth inexact Newton method, reduced the amount of calculation, under certain assumptions, prove the convergence of the algorithm and numerical results show that the algorithm is feasible and effective.