Optimisation Geometry

优化几何结构

• 批准号: DP140103163
• 负责人: Prof Jonathan Manton
• 金额: $ 25.73万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-01-01 至 2017-09-01
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140103163
• 关键词: Optimisation; Geometry

Signal processing is an enabling technology for multi-billion dollar industries including broadband connections, medical imaging devices and automotive collision avoidance systems. A key component is real-time optimisation. While various aspects of real-time optimisation have been studied extensively, especially under the banner of adaptive signal processing, the general (non-adaptive) problem will be studied here from a geometric viewpoint. Morse theory and other tools from differential topology will be used to understand the inherent complexity of real-time optimisation problems and to develop novel numerical algorithms for classes of real-time optimisation problems having widespread applicability.

信号处理是数十亿美元行业的一项使能技术，包括宽带连接、医疗成像设备和汽车防撞系统。一个关键的组成部分是实时优化。虽然实时优化的各个方面已经被广泛研究，特别是在自适应信号处理的旗帜下，一般（非自适应）的问题将在这里从几何的观点进行研究。莫尔斯理论和其他工具，从微分拓扑将被用来了解实时优化问题的固有复杂性，并开发新的数值算法类实时优化问题具有广泛的适用性。