Next Generation Newton-type Methods with Minimum Residual Solver (2025-2028)

Optimisation methods play a crucial role in many applications. Among them, Newton-type algorithms hold a special place due to their desirable properties. However, the underlying challenge remains effective solution of their complex subproblems. Leveraging recent advances in numerical linear algebra, this project aims to address this challenge directly and revolutionise Newton-type algorithms for diverse optimisation scenarios. The project is expected to pioneer new theory and open-source implementations that hold the potential to reshape the landscape of optimisation research. Among the benefits are facilitating the development of effective optimisation algorithms for machine learning and enhancing knowledge extraction from modern datasets.