Geometry in projection methods and fixed-point theory

投影方法和不动点理论中的几何

• 批准号: DP200100124
• 负责人: A/Prof Vera Roshchina
• 金额: $ 8.42万
• 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: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-01-01 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100124
• 关键词: Geometry; projection; methods; fixed; point

This project aims to resolve mathematical challenges arising from problems with specific structure typical for key modern applications, such as big data optimisation, chemical engineering and medical imaging. We focus on developing new mathematical tools for the analysis of projection methods and accompanying fixed point theory, specifically targeting the refinement of the geometric intuition for algorithm design techniques to inform the implementation of optimal methods for huge-scale optimisation problems.

该项目旨在解决现代关键应用（如大数据优化、化学工程和医学成像）中典型的特定结构问题所带来的数学挑战。我们专注于开发新的数学工具，用于分析投影方法和伴随的不动点理论，特别是针对算法设计技术的几何直觉的细化，以告知大规模优化问题的最优方法的实施。