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.
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
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
Harmonic analysis: function spaces and singular integral operators. This project advances knowledge in harmonic analysis to new settings such as dyadic and multiparameter theories, Laplacian-like operators, and rough singular integrals. Outcomes will be solutions to long-standing problems, training of researchers, strong links with international researchers and enhancement of Australia's reputation in mathematics.
There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
The paradox of choice: Unravelling complex superannuation decisions. Australia has been a world-leader in retirement savings policy, but there remains a pervasive lack of understanding about how best to communicate complex financial information to decision-makers, along with a push by government for clearer disclosure and greater financial literacy. This project will inform regulators and the superannuation industry on how choices are made and how to present clearer, better-designed information ....The paradox of choice: Unravelling complex superannuation decisions. Australia has been a world-leader in retirement savings policy, but there remains a pervasive lack of understanding about how best to communicate complex financial information to decision-makers, along with a push by government for clearer disclosure and greater financial literacy. This project will inform regulators and the superannuation industry on how choices are made and how to present clearer, better-designed information to be understood by ordinary participants, thus encouraging active, well-informed participation rather than passive 'default' decisions. More efficient investment and benefit choices will improve the economic welfare of retirees, reduce the burden on the working-age population and improve fiscal sustainability.Read moreRead less
Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for ....Risk Measures and Management in Finance and Actuarial Science Under Regime-Switching Models. New models for assessing and managing risk of financial products will place Australia at the forefront of risk management. The work will also sustain the competitive edge of Australia as one of the major financial centres in the Asia-Pacific region through enhancing both the theory and practice of financial risk management. The project outcome will also benefit to the country in other areas of risk, for example, environment risk, climate change, and energy and security problems.Read moreRead less