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
Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of poi ....Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of points on the sphere, including spherical designs.Read moreRead less
Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex ....Nonsmooth Optimization in Constrained Spline Interpolation. Traditional methods based on standard calculus may not work for optimization problems with constraints; however, such problems can be reformulated as nonsmooth problems that need special treatment. The project aims to approach several important problems in constrained spline interpolation and approximation, from the perspective of nonsmooth optimization. The research, which builds upon a recent breakthrough in the approach to the convex best interpolation by the applicant and his collaborators, is expected to provide fundamental theory for Newton-type methods being used for these problems with a vast number of applications in data fitting and curve and surface design.Read moreRead less
Stochastic Scheduling for Production and Delivery of Perishable Products with Imperfect Information. Australia has a wide range of industries producing perishable goods such as wheat, fruit, vegetables, meat, milk, seafood and health products, as well as fashion and entertainment goods. These industries play a critical role in the Australian economy, as well as impacting on national health and the environment. This project will provide new strategies, models and techniques to increase efficiency ....Stochastic Scheduling for Production and Delivery of Perishable Products with Imperfect Information. Australia has a wide range of industries producing perishable goods such as wheat, fruit, vegetables, meat, milk, seafood and health products, as well as fashion and entertainment goods. These industries play a critical role in the Australian economy, as well as impacting on national health and the environment. This project will provide new strategies, models and techniques to increase efficiency in both the production and delivery of perishable products. The outcomes of the project will enable decision makers in industries handling perishable products to optimise the use of resources, reduce costs and waste, raise productivity and improve services. The nation will benefit with higher export income and better quality of consumer products.Read moreRead less
Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to ....Computer Assisted Research Mathematics and its Applications. The mathematics community will benefit from infusion of new computer-assisted techniques and modalities for research and training post-graduate students, both from my pure research project and through development of an associated research centre. Ultimately, this should also help more school students learn mathematics well and so play a part in addressing Australia's skill shortage. Also, the work on optimization algorithms promises to improve the performance and quality of many practical signal reconstruction methods. These are used by varied Australian industries from telecommunication to mining and by researchers in the digital arts and fields such as astronomy, physics, chemistry, bioscience, geoscience, engineering and medicine.Read moreRead less
Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk ....Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk management around natural catastrophes and long-term asset investment of pension funds. The solutions and outcomes are expected to deliver optimal resource allocation proposals and better management of risk exposure in practice.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
Pervasive Grids with Autonomic Capabilities. A grid computing system that brings together a multitude of heterogonous resources able should be able to function continuously without much intervention by a human operator. This work aims at developing techniques and tools for the monitoring and prediction of the behaviour of the core structure of a grid. In this case, the ?core? structure is a large- or a wide-area network, or a collection of such networks. The monitoring process will feed into the ....Pervasive Grids with Autonomic Capabilities. A grid computing system that brings together a multitude of heterogonous resources able should be able to function continuously without much intervention by a human operator. This work aims at developing techniques and tools for the monitoring and prediction of the behaviour of the core structure of a grid. In this case, the ?core? structure is a large- or a wide-area network, or a collection of such networks. The monitoring process will feed into the other layers in the grid fabric important information (traffic, current and possible future congestions, failures, topological variations, etc) to enable the efficient and consistent operation of the grid. This is an important research problem in grid computing
since traditional assumptions that are more or less valid in conventional high-performance computing settings break down on the Grid.Read moreRead less
A Grid-Enabled Meta-Server for Protein Threading. Grid Computing is a driver for many e-Science research projects around the world today. The project investigates the use of grid technology in building a meta-server architecture for protein threading. Protein technology problems are important for the field of bioinformatics and they also influence many industries, such as, agriculture, drug design, food science, and many more. The proposed framework can be extended to other problems in the life ....A Grid-Enabled Meta-Server for Protein Threading. Grid Computing is a driver for many e-Science research projects around the world today. The project investigates the use of grid technology in building a meta-server architecture for protein threading. Protein technology problems are important for the field of bioinformatics and they also influence many industries, such as, agriculture, drug design, food science, and many more. The proposed framework can be extended to other problems in the life sciences such as bio- and health-informatics. Projects of this nature are significant and will enable Australia to maintain its pioneering position and international reputation among other nations as leaders in Information Technology.Read moreRead less