A Projection Algorithm For Solving Variational Inequalities Problems

Variational inequalities problems for studying a wide class of optimization problems in various branches of ecology, finance, economics, engineering science et al in a unified and clear framework, for a long time, has been attracting the attention of many scholars. Since the1960s, Algorithm for solving variational inequality problems emerge in endlessly, There are some typical algorithms include Newton methods, alternating directions methods, proximal algorithms and interior-point methods, neural network and projection methods. Among them, one of the most simple and feasible method for solving variational inequality problems is projection method.This paper mainly studied the use of projection method for solving variational inequality problems. The projection methods are attractive for their simplicity and efficiency, The small amount of calculation of projection each iteration, only need to do some function calculation and to make projections onto the feasible set, so this method is suitable for solving large-scale problems. The work motivation of this paper is to improve the projection method of He Bingsheng, Drops by introducing auxiliary direction, in combination with the original drop direction to construct a more efficient drop direction, we present a new projection methods for variational inequality.Details are as follows:The first part is the introduction, the paper introduces the historical background of variational inequality problems, the commonly used algorithm for solving variational inequality problems, several important concepts and conclusion, the contents of the article structure arrangement.In the second part, we discusses some the basic knowledge of the variational inequality problems and obtains the algorithm of this paper by constructing a better drop direction, and proving its global convergence under the condition of monotone.In the third part, we presents the results of numerical experiment, throught the analysis of the results, the algorithm is verified by numerical experiments with good convergence and stability.The last part is the summary of the work for this article and its prospect for the next of work.