Nonlocal PDE-constrained optimization: Modelling and numerics

非局部偏微分方程约束优化：建模和数值

• 批准号: 2436417
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2436417
• 关键词: Nonlocal; PDE; constrained; optimization; Modelling

Optimal control involves engineering physical processes to achieve idealised outcomes, while also optimising a quality measure. A suitable landscape for its applicability is parameter learning. My focus lies in discovering controls associated with nonlocal operators; i.e., operators that input information from large clouds of points in the domain of interest. Nonlocalities add additional complexity, as existence results are limited and problem-specific, while discretisation of nonlocal terms often leads to dense and ill-conditioned systems. Consequently, I am dedicated to develop efficient and high-resolution numerical solutions to tackle nonlocal systems.

最佳控制涉及工程物理过程，以实现理想的结果，同时还优化质量措施。一个适合其适用性的景观是参数学习。我的重点在于发现与非本地操作符相关的控件;即，从感兴趣域中的大量点云输入信息的运算符。非局部性增加了额外的复杂性，因为存在性结果是有限的和特定于问题的，而非局部项的离散化往往会导致稠密和病态的系统。因此，我致力于开发高效和高分辨率的数值解决方案，以解决非局部系统。

项目成果

An integer programming model to assign patients based on mental health impact for tele-psychotherapy intervention during the Covid-19 emergency.

• DOI: 10.1007/s10729-020-09543-z
• 发表时间: 2021-06
• 期刊: Health care management science
• 影响因子: 3.6
• 作者: Miniguano-Trujillo A;Salazar F;Torres R;Arias P;Sotomayor K
• 通讯作者: Sotomayor K