Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
Next-Generation OFDM Communication Systems: Analysis and Design for the Physical Layer. Next-generation orthogonal frequency-division multiplexed (OFDM) systems represent the future of broadband wireless access technology. Such systems are vital to Australia's future infrastructure and growing economy by providing more bandwidth with greater flexibility for new broadband applications. The research outcomes from this project will help enable future OFDM systems, and thus directly benefit Austra ....Next-Generation OFDM Communication Systems: Analysis and Design for the Physical Layer. Next-generation orthogonal frequency-division multiplexed (OFDM) systems represent the future of broadband wireless access technology. Such systems are vital to Australia's future infrastructure and growing economy by providing more bandwidth with greater flexibility for new broadband applications. The research outcomes from this project will help enable future OFDM systems, and thus directly benefit Australia. Development of cutting-edge information technology know-how will enhance Australia's international ICT reputation. Valuable research training of highly-skilled Australian students is another important benefit.Read moreRead less
Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Diffe ....Fast, practical and effective algorithms for clustering with advice. To maintain a safe and healthy society, government and industry need high quality immunization and national security databases. Since we cannot afford to have duplicate, incomplete and conflicting records that refer to the same person, we unify them by identifying clusters of related records.
In the emerging field of functional genomics, diagnosis of certain diseases is enhanced by determining which genes act together. Different experimental runs might result in different clusterings of genes: we need one consensus clustering that summarizes the experimental outcomes.
Cleaning databases and combining clusterings by hand would require vast amounts of time. This project will result in faster and more accurate computational procedures.Read moreRead less
Robust Optimal Asset Liability Management via Stochastic Control Theory. The Australian federal and state governments are strongly exposed to the Australian and international investment markets, either directly or through entities such as the Future Fund, state-owned insurers and superannuation schemes. Additionally, the investment pool represented by individual Australian's superannuation savings managed by non-government organisations is significant. Robust and effective management of these ....Robust Optimal Asset Liability Management via Stochastic Control Theory. The Australian federal and state governments are strongly exposed to the Australian and international investment markets, either directly or through entities such as the Future Fund, state-owned insurers and superannuation schemes. Additionally, the investment pool represented by individual Australian's superannuation savings managed by non-government organisations is significant. Robust and effective management of these assets in order to meet future liabilities of these funds are essential to a stable Australian economy. This research has the potential to be a key component of reliable investment management, helping make Australia an important investment hub.Read moreRead less
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.Read moreRead less
Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
Discovery Early Career Researcher Award - Grant ID: DE150100240
Funder
Australian Research Council
Funding Amount
$315,000.00
Summary
Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolv ....Geometry and Conditioning in Structured Conic Problems. Conic programming allows one to model and solve large industrial problems via modern optimisation methods, such as interior-point algorithms. These methods are efficient and reliable in solving a vast number of problems, however, they fail on a relatively small but significant set of ill-posed instances, thus affecting the overall reliability of the technique. The reason for such behaviour is profound and constitutes one of the major unsolved problems in real complexity: there is no known algorithm that solves conic problems with real data in polynomial time. The project aims to develop a deep understanding of the geometry of conic problems, aiming for the resolution of this fundamental problem in computational theory.Read moreRead less
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