New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problem ....New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.Read moreRead less
Data-Driven Multistage Robust Optimization—the New Frontier in Optimization. Robust optimisation is a powerful technology for decision-making in uncertain environments. Yet, developing numerically certifiable optimisation principles and data-driven methods that can be readily implemented by common computer algorithms remains an elusive goal for multistage robust optimisation. But it is crucial for the practical use of multistage optimisation. This project aims to develop this novel mathematical ....Data-Driven Multistage Robust Optimization—the New Frontier in Optimization. Robust optimisation is a powerful technology for decision-making in uncertain environments. Yet, developing numerically certifiable optimisation principles and data-driven methods that can be readily implemented by common computer algorithms remains an elusive goal for multistage robust optimisation. But it is crucial for the practical use of multistage optimisation. This project aims to develop this novel mathematical theory and methods by extending the investigators' recent award winning advances, including the von Neumann-prizewinning Lasserre-hierarchy approach. Results will provide a foundation and technologies for making superior decisions in the pervasive presence of big data uncertainty, enhancing data-driven innovation in AustraliaRead moreRead less