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.
New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Improving train flows with connected driver advice systems. The project aims to develop new train control theory to determine the efficient movement of multiple trains, and to demonstrate a practical system for coordinating trains, on busy intercity rail corridors. Railways around the world are now deploying driver advice systems developed by the research team and the partner organisation, TTG Transportation Technology. The project is designed to enable these systems to coordinate the movements ....Improving train flows with connected driver advice systems. The project aims to develop new train control theory to determine the efficient movement of multiple trains, and to demonstrate a practical system for coordinating trains, on busy intercity rail corridors. Railways around the world are now deploying driver advice systems developed by the research team and the partner organisation, TTG Transportation Technology. The project is designed to enable these systems to coordinate the movements of many trains on a congested rail network to improve timekeeping, smooth the flow of traffic, increase capacity and reduce energy use.Read moreRead less
Building Australia's next-generation ocean-sea ice model. Ocean and sea ice models are used for predicting future ocean and climate states, and for climate process research. This project aims to bring the next generation of ocean-sea ice models to Australia and configure the models for our local priorities. The ultimate goal is to create a new coupled ocean-sea ice model for Australia that includes surface waves and biogeochemistry. The model will be optimised and evaluated on Australian facilit ....Building Australia's next-generation ocean-sea ice model. Ocean and sea ice models are used for predicting future ocean and climate states, and for climate process research. This project aims to bring the next generation of ocean-sea ice models to Australia and configure the models for our local priorities. The ultimate goal is to create a new coupled ocean-sea ice model for Australia that includes surface waves and biogeochemistry. The model will be optimised and evaluated on Australian facilities, and released for community use. These developments underpin future ocean state forecasts, sea ice forecasts, wave forecasts, decadal climate prediction and climate process studies. The project will benefit search and rescue, Defence and shipping operations, and will enhance future climate projections.Read moreRead less
Design of Tough, Durable and Corrosion-resistant Coatings. Coatings are frequently applied to components operating in harsh environments to enhance durability. Often such coatings exhibit low toughness and poor corrosion resistance that leads to premature failure. The aim of this project is to design, characterise and test innovative coatings that exhibit unique architectures based on natural materials such as teeth and nacre. It is envisaged that these coatings will be hard, tough and durable i ....Design of Tough, Durable and Corrosion-resistant Coatings. Coatings are frequently applied to components operating in harsh environments to enhance durability. Often such coatings exhibit low toughness and poor corrosion resistance that leads to premature failure. The aim of this project is to design, characterise and test innovative coatings that exhibit unique architectures based on natural materials such as teeth and nacre. It is envisaged that these coatings will be hard, tough and durable in hostile, corrosive environments, and will thus, transform industries such as manufacturing, mining and offshore oil exploration as well as enhance the lifetime of prosthetic devices.Read moreRead less
ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the ....ARC Financial Integrity Research Network. The integrity of the financial system is constantly under stress because of the development of ever more complex financial instruments, structures and strategies, and the associated research technologies that continues to accelerate worldwide. FIRN's vision is to harness the considerable strengths of Australia's internationally renowned finance, accounting and economics researchers into a research agenda to address issues concerning the integrity of the financial system. It will enable Australian research in this area to match the scale and impact of similar research in other major international financial centres, and play an essential role in placing Australia among the world's leaders in financial markets related research.Read moreRead less
Special Research Initiatives - Grant ID: SR0354466
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgradu ....Mathematics in Contemporary Science. The Mathematics in Contemporary Science Research Network brings contemporary methods of non-linear analysis and differential equations, geometric reasoning and relevant algebraic and topological ideas to enrich six application areas in modern science: Complex Systems, Computer Vision, Optimal Transportation, Nanotechnology, Physics and Shortest Networks. MiCS will develop both the mathematics and the application areas in parallel. It will focus on postgraduate training through workshops, summer schools and web based resources and build long-term international collaborations with EU networks and NSERC, NSF and EPSRC institutes as well as bringing together academic and industry leaders.Read moreRead less
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a num ....Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a number of open problems at the frontier of research in modern harmonic analysis including estimates on multilinear operators with nonsmooth kernels and advanced multiparameter theory on product spaces.Read moreRead less