Two New Parallel Split LQP-ADMM Algorithms For Solving Monotone Variational Inequalities

The algorithm for solving variational inequality problems has always been one of the hot spots in the field of optimization.With the rapid development of big data technology and the integration between disciplines,the effect of existing algorithms on a large number of problems with special structure and large scale is not ideal,so it will be very interesting to explore more focus on and effective new algorithms.Combined with the advantages of existing algorithms,this paper gives an effective algorithm for solving problems which have characteristics of differentiable and separable objective function,linear constraints and large-scale.The main research work is as follows:In Chapter 3,an accurate parallel split LQP-ADMM algorithm is proposed.The new algorithm includes a prediction step and a correction step in each iteration.In the prediction step,the LQP system is solved directly;In the correction step,first,a new descent direction is constructed,and then a new correction formula is obtained by the convex combination of the previous iteration point and a projection operator,and then the optimal step size is given.In this chapter,the convergence of the new algorithm is proved under mild assumptions.Finally,the numerical experimental results show that the computational efficiency of the new algorithm is significantly improved.In Chapter 4,an inexact parallel split LQP-ADMM algorithm is proposed.The new algorithm still includes a prediction step and a correction step in each iteration,but in the prediction step,the LQP system is no longer solved directly,but the predicted value is obtained by approximately solving the LQP system under relatively loose accuracy of criteria,and the explicit formula derived from the original LQP algorithm is directly substituted into the correction step;In the correction step,two new descent directions are reconstructed,and then a new correction formula is obtained by the convex combination of the previous iteration point and a projection operator,and then the optimal step size is given.In this chapter,under appropriate assumptions,the global convergence and the convergence rate in the sense of ergodicity of the new algorithm are proved.Finally,the numerical experimental results are used to verify its effectiveness...