Australian Laureate Fellowships - Grant ID: FL130100039
Funder
Australian Research Council
Funding Amount
$2,750,000.00
Summary
New stochastic models for Science, Economics, Social Science and Engineering. Stochastic, or random, phenomena abound in society. This project will combine advancement of the theory of stochastic models at a deep level with application to problems arising in science, economics, social science and engineering, and outreach to educate members of the public about random processes of significance in their lives.
Footprints in instance space: visualising the suitability of optimisation algorithms. Optimisation problems underpin the efficiency and effectiveness of many critical sectors (e.g., healthcare, manufacturing, and defence). The project will provide both practitioners and researchers with powerful new tools to develop a much more robust understanding of the strengths and weaknesses of a variety of optimisation algorithms.
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
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
Mathematics and computing for integrated stockyard-centric management of mining supply chains. Blended mineral products, such as coal and iron ore, make a strong contribution to Australia's economy. Blending occurs in stockpiles, so to realise product value, stockyard and supply chain operational plans must align with blend targets. This project will provide new mathematical and computational planning tools to maximise this value.