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.

Monge-Ampere型全非线性偏微分方程及其在最优运输问题中的应用是近二十年来研究的热点。最优运输是线性优化的一个主题。本计画将在非线性最佳化的Monge-Ampere型方程式上发展一个新的理论，这是一个更广泛的领域，有许多重要的应用。该项目将研究解决这个问题的基本属性，并探索进一步的现实世界的应用。该项目的成果将对偏微分方程及相关研究课题产生重大影响。