非线性变分不等式的有限维近似

非线性变分不等式的有限维近似 FINITE DIMENSIONAL APPROXIMATION OF NONLINEAR VARIATIONAL INEQUALITIES 雷晋干 Lei Jingan first-author 本文讨论在Hilbert空间H中强单调算子A与列紧算子B相组合的形如 （Au-Bu,v-u）≥0,v∈K的变分不等式的有限维近似问题,其中K为Ⅳ中的非空凸闭子集.给出了解存在的一种构造性证明.同时讨论了近似解的收敛性. Let H be Hilbert spacer KH be closed convex subset with nonempty interior points. In this paper we consider the finite dimensional approximation of the following variational inequality: （Au-Bu, v-u）≥0, v∈K, where A is a strong monotone operator, B is a compact operator on K. The existence and convergenee for approximate solutions are discussed. 变分不等式 凸子集合 集合收敛 非线性算子 Variatonal inequality Convex subset Set convergence Nonlinear operator 1987-03-01 2021-04-01 3