Research on Variational Analysis and Applications

小行星9704751 该项目将支持变分分析及其 应用.研究的特定领域将包括：非凸 非光滑集值映射的广义微分 Banach空间;鲁棒性的新刻画及其应用 无穷维Lipschitz稳定性;解的灵敏度分析 参数广义方程和变分不等式的映射; 约束泛函的离散逼近与最优控制 微分包含;不确定演化系统的鲁棒控制设计 具有硬控制和状态约束的系统。 变分分析已被公认为现代数学的一个活跃领域。 应用数学，一方面，解决大规模的 优化和相关问题，另一方面，适用于 优化和微扰的想法，以分析广泛的 数学模型在现实生活中的应用。特别是具有一种 提出的目标是将变分方法应用于反馈控制 环境应用激发的进化系统设计。

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.