Smooth Solutions to Linear Inequalities, Constrained Sobolev interpolation, and Trace Problems on Domains

线性不等式的平滑解、约束 Sobolev 插值和域上的追踪问题

• 批准号: 2247429
• 负责人: Garving Luli
• 金额: $ 22.71万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2247429&HistoricalAwards=false
• 关键词: Smooth; Solutions; Linear; Inequalities; Constrained

Solving a system of linear inequalities with parameters is essential in various applications, such as engineering, science, sociology, economics, industry, and even medicine (such as the optimal combination of drugs for efficacy and safety). The efficient algorithms on constrained interpolation can be applied to analyze big data such as Twitter data. This endeavor will help promote interdisciplinary research and improve the current computing infrastructure. Research opportunities will be provided for postdocs, graduate students, and undergraduate students.Smooth solutions to systems of linear inequalities will be addressed. Attention will also be paid to efficient algorithms for constrained interpolation by smooth functions and extension questions on arbitrary domains. The methods to be developed will revolve around common mathematical themes, such as Calderon-Zygmund decomposition, well-separated pairs, and convex optimization.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.

求解具有参数的线性不等式系统在各种应用中至关重要，例如工程、科学、社会学、经济学、工业，甚至医学（例如药物功效和安全性的最佳组合）。约束插值的高效算法可以应用于分析Twitter数据等大数据。这一努力将有助于促进跨学科研究并改善当前的计算基础设施。将为博士后、研究生和本科生提供研究机会。将讨论线性不等式系统的平滑解决方案。还将关注通过平滑函数和任意域上的扩展问题进行约束插值的有效算法。待开发的方法将围绕常见的数学主题，例如 Calderon-Zygmund 分解、分离对和凸优化。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优势和更广泛的评估进行评估，被认为值得支持。影响审查标准。