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

求解带参数的线性不等式系统在各种应用中都是必不可少的，例如工程学、科学、社会学、经济学、工业甚至医学（例如药物的有效性和安全性的最佳组合）。约束插值的有效算法可以应用于分析大数据，如Twitter数据。这一奋进将有助于促进跨学科研究，并改善当前的计算基础设施。研究机会将提供给博士后，研究生，和本科生。光滑的解决方案，系统的线性不等式将得到解决。也将注意到有效的算法约束插值光滑函数和扩展问题的任意域。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。

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.