Lagrange Multiplier Expression Methods for Optimization

优化的拉格朗日乘子表达方法

基本信息

批准号：
2110780
负责人：
Jiawang Nie
金额：
$ 35万
依托单位：
University of California-San Diego
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110780&HistoricalAwards=false
关键词：
Lagrange Multiplier Expression Methods Optimization

项目摘要

Optimization techniques are useful for solving problems in economics, telecommunications, quantum physics, and other fields. This project involves Lagrange multiplier expression methods for optimization, which are use useful in computing. The project identifies and aims to solve various research tasks from the field of optimization within computational mathematics and related areas. The research topics of this project have broad applications in many areas of STEM. The computational methodology produced by this project will be highly useful in applications such as game theory, power allocation, environment pollution control, quantum entanglement, and tensor optimization. This project will also involve training and education for young scholars.This project aims to solve various research problems in optimization relevant for the applications. Specifically, the project will involve Lagrange multiplier expressions which provide useful framework within computational mathematics. Expressing Lagrange multipliers in terms of objective and constraining functions is an important issue in optimization. Tight convex relaxation is efficient for solving computational questions. The research topics include polynomial optimization, convex algebraic geometry, moment and tensor problems, bilevel optimization, generalized Nash equilibrium problems, stochastic optimization, tensor computation, tensor optimization, and other related problems. The project will address computational questions involving polynomials, matrices, moments and tensors, frequently appearing from various applications.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.

优化技术可用于解决经济学，电信，量子物理学和其他领域的问题。该项目涉及用于优化的Lagrange乘数表达方法，这些方法用于计算。该项目确定并旨在从计算数学和相关领域的优化领域解决各种研究任务。该项目的研究主题在许多STEM领域都有广泛的应用。该项目生产的计算方法将在游戏理论，功率分配，环境污染控制，量子纠缠和张量优化等应用中非常有用。该项目还将涉及对年轻学者的培训和教育。该项目旨在解决与应用相关的优化方面的各种研究问题。具体而言，该项目将涉及Lagrange乘数表达式，这些表达式在计算数学中提供了有用的框架。在客观和约束功能方面表达Lagrange乘数是优化的重要问题。紧密的凸松弛可以有效地解决计算问题。研究主题包括多项式优化，凸代数几何形状，力矩和张量问题，二聚体优化，广义NASH平衡问题，随机优化，张量计算，张量优化和其他相关问题。该项目将解决涉及多项式，矩阵，时刻和张量的计算问题，经常出现在各种应用程序中。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智力优点和更广泛影响的评估评估标准来通过评估来支持的。