使用Kantorovich定理计算变分不等式的可靠解  

COMPUTING THE VALIDATED SOLUTION OF VARIATIONAL INEQUALITY PROBLEM BY USING KANTOROVICH THEOREM

作　　者：牛欣[1] 江正华[2] 

机构地区：[1]合肥学院数学与物理系,合肥230601 [2]南京大学数学系,南京210093

出　　处：《高等学校计算数学学报》2017年第3期250-266,共17页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学数学天元基金(No.11526071);安徽高校自然科学研究重点项目(No.KJ2016A592)资助

摘　　要：1引言 给定R^n中非空子集Ω和函数F：R^n→R^n，变分不等式问题（简记为VIP（Ω，F））是指寻求向量x＊∈Ω满足( y-x * ) T F( x * ）≥0，In this note, we extend the NewtomKantorovich theorem to validate the convergence of the Newton-Josephy method for solving variational inequality problems. All the conditions can be tested in digital computer. Moreover, the validation delivers automatically the existence domain of the solution and the error estimate, by which one can compute the validated solution of the problems. The ideas are illustrated by numerical results.

关 键 词：变分不等式问题 H定理 计算 R^N 非空子集 和函数 VIP 向量 

分 类 号：O24[理学—计算数学]