Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE180100923
Funder
Australian Research Council
Funding Amount
$348,575.00
Summary
Efficient second-order optimisation algorithms for learning from big data. This project aims to apply a diverse range of scientific computing techniques to design and implement new, second-order methods that can surpass first-order alternatives in the next generation of optimisation methods for large-scale machine learning (ML). Scalable optimisation methods are now an integral part ML in the presence of “big data”. While the development of efficient first-order methods has grown in the ML comm ....Efficient second-order optimisation algorithms for learning from big data. This project aims to apply a diverse range of scientific computing techniques to design and implement new, second-order methods that can surpass first-order alternatives in the next generation of optimisation methods for large-scale machine learning (ML). Scalable optimisation methods are now an integral part ML in the presence of “big data”. While the development of efficient first-order methods has grown in the ML community, second-order alternatives have largely been ignored. The project expects to facilitate the development of more effective ML algorithms for extraction of knowledge from large data sets.Read moreRead less