New Frontiers in Large-Scale Polynomial Optimisation

多项式优化在工程和应用数学的许多领域中无处不在。用于大规模多项式问题的数学方法和算法尚未得到充分发展，限制了它们对现实问题的适用性。本项目旨在发展大规模多项式优化的数学基础和计算方法。通过使用新颖的代数几何理论和凸优化的创新组合，该项目期望为解决这些问题产生新的知识和工具。预期的结果包括新一代大规模优化技术，为澳大利亚的工业和国际研究地位提供重大利益。

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.