Applied Variational Analysis: Structure, Regularity, and Algorithms

应用变分分析：结构、规律和算法

• 批准号: 0504032
• 负责人: Adrian Lewis
• 金额: $ 27.54万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0504032&HistoricalAwards=false
• 关键词: Applied; Variational; Analysis; Structure; Regularity; Applied; Variational; Analysis; Structure; Regularity

Traditional calculus is a central scientific tool for understanding phenomena varying smoothly in time and space. Variational analysis extends the reach of calculus beyond smooth scenarios to optimization problems in a wide range of modern disciplines, including management science, control engineering, and economics. This project bridges the gulf between an existing, well-developed theory on the one hand, and much less-developed concrete applications on the other. Nonsmooth geometry is challenging: unlike in calculus, the shapes and structures of interest have corners and sharp ridges, frustrating traditional mathematical and computational analysis. This project will relate the difficulty of solving a nonsmooth optimization problem to a crucial theoretical notion of its "regularity". In the longer term, the project will pursue effective computational solution algorithms for nonsmooth optimization. A fertile interplay between innovative theory, high-impact engineering applications, and reliable solution methods is central to the project's success. Graduate students, international dissemination, and interdisciplinary collaborations with institutes of computing, control engineering, and industrial sciences, will all play important roles in the project's development.

传统演算是一种中心科学工具，用于理解在时间和空间上平稳变化的现象。 各变化分析将微积分的影响范围扩展到平滑的场景之外，并在包括管理科学，控制工程和经济学在内的广泛现代学科中的优化问题。 该项目一方面桥接了现有的，发达的理论，另一方面桥接了较不发达的混凝土应用之间。 非平滑的几何形状具有挑战性：与微积分不同，感兴趣的形状和结构具有角落和尖锐的山脊，使传统的数学和计算分析令人沮丧。 该项目将将解决非平滑优化问题的困难与其“规律性”的关键理论概念联系起来。 从长远来看，该项目将采用有效的计算解决方案算法，以进行非平滑优化。 创新理论，高影响力的工程应用和可靠的解决方案方法之间的肥沃相互作用是该项目成功的核心。 研究生，国际传播和与计算，控制工程和工业科学学院的跨学科合作将在该项目的开发中发挥重要作用。