Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science

该项目旨在为数据科学中使用的优化算法的分析和开发开发数学基础。尽管机器学习软件包现在普遍使用，但它们通常依赖于一些来自数学优化的算法，而这些算法并没有得到正确的理解。通过超越费耶尔单调算法的传统领域，该项目希望发展所需的数学理论，以严格证明使用这种算法的合理性，从而确保它们所产生的决策工具的完整性。这一数学框架还有望产生新的优化算法，使医疗保健和网络安全等数据科学的消费者受益。

This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the mathematical theory required to rigorously justify the use of such algorithms and thereby ensure the integrity of the decision tools they produce. This mathematical framework is also expected to produce new algorithms for optimisation which benefit consumers of data science such as the health-care and cybersecurity sectors.