Variational Analysis and its Applications

这项研究项目致力于变分分析的理论和应用，变分分析是应用数学中一个活跃的领域，主要关注与优化相关的问题。它还应用变分技术来研究一系列可能不属于变分性质的问题。由于非光滑结构经常和自然地出现在分析和优化中，广义微分的构造和技术是变分分析及其应用的核心。该项目将主要致力于发展变分分析和广义微分的基本理论，并将其应用于优化、控制、稳定、力学和经济中的重要问题。各种活动需要最优决策，包括高性能计算、制造、环境和全球变化等。变分分析涉及优化的数学方法，在工程、经济和其他现代科学技术领域的复杂系统的许多应用中发挥着至关重要的作用。这项研究项目将集中于开发和应用有效的数学技术，以在复杂结构的系统中发现最优解。它尤其涉及开发最优控制的新方法。该奖项由数学科学司和社会、行为和经济科学局共同资助，作为数学科学优先领域的一部分。

This research project is devoted to the theory and applications of variational analysis, an active area in applied mathematics primarily concerned with optimization-related problems. It also applies variational techniques to the study of a broad range of problems that may not be of a variational nature. Since nonsmooth structures frequently and naturally appear in analysis and optimization, constructions and techniques of generalized differentiation lie at the heart of variational analysis and its applications. The project will mainly deal with developing the basic theory of variational analysis and generalized differentiation, with applications to important problems in optimization, control, stability, mechanics, and economics.Optimal decisions are required in various activities, including high-performance computing, manufacturing, environment and global change, etc. Variational analysis concerns mathematical methods of optimization that play a crucial role in many applications to complex systems in engineering, economics, and other areas of modern science and technology. This research project will focus on the development and application of efficient mathematical techniques for discovering optimal solutions in systems with complex structures. It particularly involves developing new methods of optimal control. This award is being jointly funded by the Division of Mathematical Sciences and the Directorate for Social, Behavioral, and Economic Sciences as part of the Mathematical Sciences Priority Area.