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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、量子物理和其他领域的问题。该项目涉及用于优化的拉格朗日乘子表达方法，这些方法在计算中很有用。该项目确定并旨在解决计算数学及相关领域优化领域的各种研究任务。该项目的研究课题在STEM的许多领域都有广泛的应用。该项目产生的计算方法将在博弈论、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中的各种研究问题。具体来说，该项目将涉及拉格朗日乘子表达式，它为计算数学提供了有用的框架。用目标函数和约束函数来表达拉格朗日乘子是优化中的一个重要问题。紧凸松弛对于解决计算问题非常有效。研究主题包括多项式优化、凸代数几何、矩和张量问题、双层优化、广义纳什均衡问题、随机优化、张量计算、张量优化以及其他相关问题。该项目将解决涉及多项式、矩阵、矩和张量的计算问题，这些问题经常出现在各种应用程序中。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。