Discovery Early Career Researcher Award - Grant ID: DE210101056
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explain ....Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explaining the power and limitations of these methods when compared with existing approaches. Possible benefits include safer and more reliable complex engineered systems, such as the power grid or interacting autonomous vehicles, verified by methods built on those developed in the project.Read moreRead less
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. 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