An Interior-point Algorithm For Box-constrained And Monotone Variational Inequality Problems

In this paper,we present an interior-point algorithm for the box-con-strained and monotone variational inequality problems on finite dimensi-on space and bound sets.In the paper, we first construct a strong monotoneproblem,obtain a search direction through projection and then presenta descend algorithm for it. On the basic of it, we present the interior-point algorithm. After that, we introduce its application in compleme-ntarity problems. The result of numerical experiment indicates theefficiency of the algorithm which is presented in this paper. The paper contain five parts. In Section One,some methods for solv-ing variational inequality problems are introduced and the shortage ofthem are also analysed. In Section Two,some basic definiens and theoriesof variational inequality are introduced. Section Three is the importantpart of this paper, in which the interior-point algorithm for solvingthe box-constrained and monotone variational inequality problems aredescribed in details.And the convergence of them are proved. Section Fouris numerical experiment,the results show the effectiveness of theproposed algorithms. In Section Five ,we conclude the paper.