一类含参广义方程的隐函数定理及其应用

动机于现有广义方程模型在非光滑优化应用中的局限性，本项目拟在隐函数定理框架下研究一类由两个集值映射之和确定的参数广义方程(PGE)解映射的适定性性质。考虑到参数广义方程的随机模型(PSGE)与非光滑随机均衡问题之间的密切关系，我们将结合变分分析与随机规划的理论，拟对(PSGE)解映射在广义概率测度逼近下的存在性及稳定性展开研究，预期对随机优化的扰动分析理论做出贡献。

Due to the limitation of existed generalized equation models in application of nonsmooth optimization, this proposal plans to study the well-posedness properties of the solution mapping associated to a class of parametric generalized equations determined by the sum of two set-valued functions under the paradigm of implicit function theorems. Considering the close relationship between parametric stochastic generalized equations and nonsmooth stochastic equilibrium problems, by virtue of combining the techniques of variational analysis and stochastic programming, we will investigate the existence and stability theory of the solution mapping of (PSGE) under the variation of general probability measure and expect to make contributions to the perturbation theory of stochastic optimization.