Exploring and exploiting structures in nonsmooth and global optimization problems. Global and non-smooth optimisation problems are among the most challenging in optimisation. Such problems arise in optimisation of many systems including financial, business and engineering systems. Achieving optimal performance of these systems will provide considerable commercial and environmental benefits. This project aims to develop new approaches to global and non-smooth optimisation using their special stru ....Exploring and exploiting structures in nonsmooth and global optimization problems. Global and non-smooth optimisation problems are among the most challenging in optimisation. Such problems arise in optimisation of many systems including financial, business and engineering systems. Achieving optimal performance of these systems will provide considerable commercial and environmental benefits. This project aims to develop new approaches to global and non-smooth optimisation using their special structures. The outcomes of this project will be new approaches to practical problems and ready-to-implement algorithms. It will major benefit to Australian society whilst also facilitating excellent international collaboration.Read moreRead less
Optimal Deployment of Wireless Sensor Networks. Wireless sensor networks consist of coordinated sensing devices that offer us new ways to understand and interact with the physical world. Australia is a leading player in developing such networks. For a given technology, the key to both optimising the quality of area monitoring and minimising the cost of a sensor network lies in deciding how best to deploy the sensors. We aim to develop powerful new methods to get the best performance from a plann ....Optimal Deployment of Wireless Sensor Networks. Wireless sensor networks consist of coordinated sensing devices that offer us new ways to understand and interact with the physical world. Australia is a leading player in developing such networks. For a given technology, the key to both optimising the quality of area monitoring and minimising the cost of a sensor network lies in deciding how best to deploy the sensors. We aim to develop powerful new methods to get the best performance from a planned sensor network. This will enhance Australia's research role in this area and directly benefit applications such as national security and environmental monitoring.
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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
Novel decomposition methods for large scale optimisation. This project will develop more effective problem decomposition methods that are critical for handling large scale problems (problems with up to several thousands of variables). The project will benefit practitioners from many different fields, and will put Australia at the very forefront of international research for large scale optimization.
Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unit ....Unlocking the potential for linear and discrete optimisation in knot theory and computational topology. Computational topology is a young, energetic field that uses computers to solve complex geometric problems, such as whether a loop of string is tangled. Such computations are becoming increasingly important in mathematics, and applications span biology, physics and information sciences, however many core problems in the field remain intractable for all but the simplest cases. This project unites geometric techniques with powerful methods from operations research, such as linear and discrete optimisation, to build fast, powerful tools that can for the first time systematically solve large topological problems. Theoretically, this project has significant impact on the famous open problem of detecting knottedness in fast polynomial time.Read moreRead less