解变分不等式的次梯度二次投影算法  

The Subgradient Double Projection Algorithm for Solving Variational Inequalities

作　　者：郑莲[1] 苟清明[1] 

机构地区：[1]长江师范学院数学与计算机科学学院,重庆408100

出　　处：《应用数学学报》2014年第6期968-975,共8页Acta Mathematicae Applicatae Sinica

基　　金：重庆市教委重点资助项目(kj111309)

摘　　要：运用凸函数的次梯度来构造包含可行集的半空间,将已有变分不等式的二次投影算法的投影域进行改进.每次迭代,已有算法的第二次是投影到可行集与半空间的交集上,而新的二次投影算法是投影到两个半空间的交集上.当可行集为一般的闭凸集时,该算法的投影更容易计算.在较弱的条件下,讨论了算法的全局收敛性.We construct a new halfspace by the subgradient of a convex function, which contains the feasible set of variational inequalities （Ⅵ）, and the projection regions of the existing double projection methods for solving the VI are modified. At each iteration, the new algorithm replaces the second projection onto the intersection set of the feasible set and a halfspace with the intersection set of two halfspaces. When the feasible set is a general closed and convex set, our projection is more easily executed. Our method is proved to be globally convergent to a solution of VI under very mild assumptions.

关 键 词：变分不等式 半空间 二次投影算法 次梯度 Armijo线性搜寻 收敛性 

分 类 号：O177.92[理学—数学]