Variational Analysis: Theory, Algorithms, and Applications

变分分析：理论、算法和应用

基本信息

批准号：
2204519
负责人：
Boris Mordukhovich
金额：
$ 25万
依托单位：
Wayne State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-09-01 至 2025-08-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2204519&HistoricalAwards=false
关键词：
Variational Analysis Theory Algorithms Applications

项目摘要

This project aims to investigate mathematical aspects of optimization and control. The research will focus on practical models in engineering design of control systems, socioeconomics, robotics, nanotechnology, and behavioral sciences. Investigating and solving such models using advanced mathematical methods will promote the progress of science and enhance national security. Understanding mobile robot modeling, dynamic models for nanoparticles in nanotechnology, and marine surface vehicle modeling will be particularly important for national defense. The research will provide opportunities for training Ph.D. students, including those from underrepresented groups. The research aims to develop variational analysis methods and generalized differentiation, emphasizing numerical algorithms and applications. The research will focus on a broad spectrum of theoretical and algorithmic issues in first-order and second-order variational techniques with applications to various problems. Specifically, the investigator will focus on constrained optimization with smooth and nonsmooth data in finite and infinite dimensions, bilevel programming and facility location, variational inequalities and equilibrium systems, new challenging classes of problems in dynamic optimization and optimal control with irregular constraints, parabolic quasi-variational inequalities, and stability of nonsmooth control systems and feedback stabilization. The first-order and second-order generalized differentiation results will be applicable to design novel numerical algorithms to solve optimization, control, and related problems. The algorithms will be implemented in practical modeling.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目旨在研究优化和控制的数学方面。该研究将重点介绍控制系统，社会经济学，机器人技术，纳米技术和行为科学的工程设计实用模型。使用高级数学方法调查和解决此类模型将促进科学的进步并增强国家安全。了解移动机器人建模，纳米技术中纳米颗粒的动态模型以及海面车辆建模对于国防尤其重要。该研究将为培训博士提供机会。学生，包括来自代表性不足的团体的学生。该研究旨在开发分析方法和广义分化，强调数值算法和应用。该研究将集中于一阶和二阶变异技术中的一系列理论和算法问题，并应用了各种问题。具体而言，研究人员将通过有限和无限维度，双重编程和设施的位置，变异不平等和平衡系统，动态优化中的新型问题类别的新挑战性类别的问题和不规则约束的最佳控制类别的新型挑战性类别的稳定性稳定性，寄生虫Quasi-quasiatirational Empory和NONSONSTION和NONSONSERIANS和NONSONSTIALION和NONONSONSTAILION和NONSONSTIAL。一阶和二阶广义分化结果将适用于设计新型的数值算法以解决优化，控制和相关问题。该算法将在实际建模中实施。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评论标准来评估值得支持的。