New mathematics for multi-extremal optimization and diffusion tensor imaging

多极值优化和扩散张量成像的新数学

• 批准号: DP180100745
• 负责人: Prof Vaithilingam Jeyakumar
• 金额: $ 27.08万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180100745
• 关键词: New; mathematics; multi; extremal; optimization

This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.

该项目旨在建立半代数优化问题的可数值证明的数学理论和方法。可数值证明的优化原理和技术对于优化技术的实际应用至关重要，因为它们可以很容易地通过常见的计算机模型和算法来实现。然而，对于现代科学和医学中常见的多极值、半代数优化问题，不存在这样的方法。该项目的预期成果包括增强扩散张量成像的优化方法，这是脑科学中的一项新兴技术。