New mathematics for multi-extremal optimization and diffusion tensor imaging

该项目旨在建立半代数优化问题的数值可验证的数学理论和方法。数值可验证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，还没有这样的方法。该项目的预期成果包括弥散张量成像的增强优化方法，这是脑科学中的一项新兴技术。

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.