变分不等式的一类二次投影算法

The Framework of Double Projection Algorithm for Variational Inequalities

通过构造的一类严格分离当前点与解集的超平面得到了一类解伪单调变分不等式的修正二次投影算法,该算法对He Yiran的算法进行了修正.从而建立了解伪单调变分不等式二次投影算法的一种框架结构.证明了该算法生成的无穷序列具有的全局收敛性,在具备某种局部误差界和Lipchitz连续条件下给出了收敛率分析.并给出了该算法的数值演算结果.

We present a modification of a double projection Mgorithm proposed by Yiran He for solving pseudomonotone variational inequalities. The main modification is obtained a class of hyperplane, which can separate the current iterate from the solution of the variational inequalities. To use these hyperplanes, we construct the framework of double projection algorithm for solving variational inequalities. Our method is proven to be globally convergent under very mild assumptions. If in addition a certain error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments are proposed too.