Methods of Variational Analysis in Optimization, Equilibria, and Control

该项目涉及发展变分分析的新方法及其在优化，平衡和控制中的各种问题的应用。 由于现代变分原理和技术本质上与非光滑数据的模型和问题有关，因此很大一部分研究涉及非光滑函数、集合和集值映射的一阶和二阶广义微分理论。 所得到的方法和结果的广义微分将适用于推导新的最优性和次优性条件和灵敏度/稳定性特征的问题的数学规划，优化和平衡问题的平衡约束，最优控制的发展包含和偏微分和泛函微分方程，该项目的主要目标是发展最优化、变分分析和最优控制的先进技术在机械、经济、工程、环境科学、这是一个非常具有挑战性的问题，这需要发展新的数学方法来处理非经典对象和模型以及复杂的控制系统。 该研究将特别关注公共环境的福利经济学模型，以及涉及寡头垄断市场的经济，不确定性下控制系统的反馈设计，以及其他实际问题的应用。

The project deals with developing new methods of variational analysis and their applications to various problems in optimization, equilibria, and control. Since modern variational principles and techniques intrinsically relate to models and problems with nonsmooth data, a large part of the research concerns generalized differentiation theory of the first and second order for nonsmooth functions, sets, and set-valued mappings. The obtained methods and results of generalized differentiation will be applied to deriving new optimality and suboptimality conditions and sensitivity/stability characterizations in problems of mathematical programming, optimization and equilibrium problems with equilibrium constraints, optimal control of evolution inclusions and partial differential and functional differential equations, etc. The primary goal of this project is to develop applications of advanced techniques of optimization, variational analysis, and optimal control to practical problems arising in mechanics, economics, engineering, environmental science, etc. This is a very challenging issue, which requires the development of new mathematical methods dealing with non-classical objects and models as well as with complex control systems. The research will particularly concern models of welfare economics with public environment and also economies involving oligopolistic markets, feedback design of control systems functioning under uncertainty, and other applications to real-life problems.