随机严格单调映射和随机单调映射的线性互补

Linear Complementary Problem of Stochastic Strictly Monotone Mapping and Stochastic Monotone Mapping

为研究一类随机互补问题的解集问题,引入了随机严格单调映射和随机单调映射,并且给出1个映射为随机严格单调映射与随机单调映射的充要条件。研究了当映射F(x,ω)为随机严格单调映射时的随机线性互补问题解的情况,并且证明在该条件下其期望残差方法的解集是非空有界的。

To solve the solution of a stochastic complementary problem, we define the stochastic strictly mono- tone mapping and stochastic monotone mapping and give the sufficient and necessary conditions of them. The solution of stochastic linear complementary problem is studied when involving mapping F（x,w） is stochastic strictly monotone mapping. It is concluded that the solution of ERM is nonempty and bounded when the invol- ving F（x, w） is stochastic strictly monotone mapping.