New Frontiers in Large-Scale Polynomial Optimisation

大规模多项式优化的新领域

• 批准号: DE240100674
• 负责人: Dr Mareike Dressler
• 金额: $ 25.58万
• 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 Early Career Researcher Award
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-01-01 至 2026-12-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE240100674
• 关键词: New; Frontiers; Large; Scale; Polynomial

Polynomial optimisation is ubiquitous in many areas of engineering and applied mathematics. The mathematical methods and algorithms used for polynomial problems of large size are not sufficiently developed, limiting their applicability for real-world problems. This project aims to develop a mathematical foundation and computational methods for large-scale polynomial optimisation. By using an innovative combination of a novel theory of algebraic geometry and convex optimisation, this project expects to generate new knowledge and tools for solving these problems. Anticipated outcomes include a new generation of large-scale optimisation technologies, providing significant benefit to Australia's industries and international research standing.

在工程和应用数学的许多领域，多项式优化无处不在。用于大尺寸的多项式问题的数学方法和算法没有充分开发，从而限制了它们对现实问题的适用性。该项目旨在为大规模多项式优化开发数学基础和计算方法。通过使用一种新颖的代数几何学和凸优化理论的创新组合，该项目希望生成新的知识和工具来解决这些问题。预期的结果包括新一代的大规模优化技术，为澳大利亚的行业和国际研究地位提供了巨大的好处。