Research on Variational Analysis and Applications

9704751该项目将支持变分分析及其应用的研究。具体的研究领域将包括：Banach空间之间非光滑映射和集值映射的非凸广义微分；无穷维鲁棒Lipschitzian稳定性的新刻画和应用；参数广义方程和变分不等式解映射的灵敏度分析；约束泛函微分包含的离散逼近和最优控制；以及具有硬控制和状态约束的不确定发展系统的鲁棒控制设计。变分分析已被公认为现代应用数学的一个活跃领域，它一方面处理大规模优化和相关问题，另一方面将优化和摄动思想应用于分析现实应用中出现的广泛的数学模型。特别是，建议的目标之一是将变分方法应用于受环境应用激励的进化系统的反馈控制设计。

9704751 Mordukhovich This project will support research on variational analysis and its applications. Particular areas of research will include: nonconvex generalized differentiation of nonsmooth and set-valued mappings between Banach spaces; new characterizations and applications of robust Lipschitzian stability in infinite dimensions; sensitivity analysis of solution maps for parametric generalized equations and variational inequalities; discrete approximations and optimal control of constrained functional differential inclusions; and robust control design of uncertain evolutionary systems with hard control and state constraints. Variational analysis has been recognized as an active area of modern applied mathematics that, on one hand, deals with solving large-scale optimization and related problems and, on the other hand, applies optimization and perturbation ideas to the analysis of a broad spectrum of mathematical models arising in real-life applications. In particular, one of the proposal goals is to apply variational methods to feedback control design of evolutionary systems motivated by environmental applications.