Fully nonlinear partial differential equations in optimisation and applications

全非线性偏微分方程的优化及应用

• 批准号: DE140101366
• 负责人: A/Prof Jiakun Liu
• 金额: $ 26.32万
• 依托单位: University of Wollongong
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-20 至 2019-07-18
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE140101366
• 关键词: Fully; nonlinear; partial; differential; equations

Fully nonlinear partial differential equations of Monge-Ampere type and their applications in optimal transportation have been studied intensively in the past two decades. Optimal transportation is a subject in linear optimisation. This project will develop a new theory on Monge-Ampere type equations in nonlinear optimisation, which is a much broader area with many significant applications. This project will investigate fundamental properties of solutions to this problem and explore further real-world applications. The outcomes of this project will have a substantial impact on partial differential equations and related research subjects.

在过去的二十年里，Monge-Ampere型完全非线性偏微分方程及其在最优运输中的应用得到了广泛的研究。最优运输是线性最优化中的一个主题。这个项目将发展一种新的关于非线性最优化中的Monge-Ampere型方程的理论，这是一个具有许多重要应用的更广泛的领域。这个项目将研究这个问题的解决方案的基本性质，并探索进一步的现实世界应用。该项目的成果将对偏微分方程组及相关研究课题产生重大影响。