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
Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will devel ....Perturbation and approximation methods for linear operators with applications to train control, water resource management and evolution of physical systems. Linear equations are used to solve practical problems. In realistic problems the equations and their solutions depend on parameters obtained by measurement of physical quantities and on data derived from observations and experiments. Changes to the values of the key parameters will lead to changes in the solutions. This project will develop methods to better understand the relationships between the key parameters and the solutions and will apply the new insights to practical problems such as the minimization of fuel consumption in trains, optimal resource management in water supply systems and the evolution of physical systems.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
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an inte ....Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an international collaboration which will improve Australia's ability to participate effectively in international research and innovation and to produce globally competitive mathematical technologiesRead moreRead less
Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national be ....Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national benefits is that the proposed research collaboration will provide extremly fertile ground for training postdoctoral researchers and graduate students in one of the most applicable areas of mathematics.Read moreRead less
Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable condition ....Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable conditions for a global optimum is a serious limitation. This project will develop verifiable such global optimality conditions for many classes of these problems. A new methodology, functional abstract convexity, developed by CIs and has shown promising results, will be extended and applied for solving these problems.Read moreRead less
A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. ....A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. Since global optimization technology is used in many scientific disciplines and modern industrial applications, the research will make many Australian science and industries more competitive. Our research also represents a program of high profile international collaborations that will improve Australia's ability to produce internationally competitive optimization technology.
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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