Special Research Initiatives - Grant ID: SR0354727
Funder
Australian Research Council
Funding Amount
$20,000.00
Summary
Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mat ....Mathematics for Government, Industry and Community -- The *Magic* Network. The *Magic* network will promote the use of mathematics by government, industry and community to analyse real problems and implement practical solutions. It will connect the most promising young Australian mathematicians to experienced researchers with strong research teams linked directly to the broader community. Our program will demand research excellence, emphasise a sustainable society, support outstanding young mathematicians and create opportunities for promising postgraduate students. We will offer scholarships for professional development and fund research visits and exchanges. *Magic* will provide tangible incentives for young Australian mathematicians and a new generation of researchers and research leaders.Read moreRead less
Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions ....Construction of utility functions from observations of consumer behaviour with application to resource modelling and water management strategies. The optimisation techniques developed will be on the forefront of applied mathematical sciences and will increase the prestige of the Australian mathematical community. The expected results will also be of value because they can be used to improve the CGE modelling technique. The implementation of the CGE model of one of Victoria's agricultural regions will be used to improve the accuracy of regional economic models and will contribute to efficient regional resource management. This has the potential to positively affect the economic growth and employment in the region. The expected outcomes of the project are especially important taking into account the need for predicting the socio-economic consequences of the 1994 COAG water reforms. Read moreRead less
Designing minimum-cost networks that are robust and avoid obstacles. The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical ....Designing minimum-cost networks that are robust and avoid obstacles. The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical considerations such as surviving local connectivity failures and avoiding pre-existing obstacles. These are recognised as mathematically challenging problems. Current approaches employ restrictive models that do not capture the flexibility of modern infrastructure networks. This project aims to develop geometric design methods using variable ‘Steiner points’, leading to fast algorithms for optimally solving these problems.Read moreRead less
Distributed Optimisation without Central Coordination. This project will develop the mathematical foundations for discovery and analysis of iterative methods for optimisation problems in distributed computing systems. Most methods in distributed optimisation were not designed for distributed computing, rather they were adapted for purpose post-hoc. By building on recent advances in monotone operator splitting, this project expects to develop a mathematical theory for decentralised optimisation a ....Distributed Optimisation without Central Coordination. This project will develop the mathematical foundations for discovery and analysis of iterative methods for optimisation problems in distributed computing systems. Most methods in distributed optimisation were not designed for distributed computing, rather they were adapted for purpose post-hoc. By building on recent advances in monotone operator splitting, this project expects to develop a mathematical theory for decentralised optimisation algorithms specially designed for distributed systems. The framework is expected to produce a suite of algorithms, each customised to exploit a specific network configuration. The project will provide significant benefits in distributed machine learning applications such as federated learning.Read moreRead less
Derivative free algorithms for large scale nonsmooth and global optimization and their applications. The outcomes expected from this research fall broadly into two categories: 1) the development of a new class of effective readily implementable derivative free techniques for large scale non-smooth and global optimisation and 2) the development of new algorithms based on derivative free optimization techniques for solving data mining, resource allocation problems and some problems in bioinformati ....Derivative free algorithms for large scale nonsmooth and global optimization and their applications. The outcomes expected from this research fall broadly into two categories: 1) the development of a new class of effective readily implementable derivative free techniques for large scale non-smooth and global optimisation and 2) the development of new algorithms based on derivative free optimization techniques for solving data mining, resource allocation problems and some problems in bioinformatics. In particular, the application of these techniques to molecular biology and cluster analysis will be very important for the development of competitive technologies for Australia.
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Approximate bundle methods in nonsmooth optimisation and their applications in some complex systems. Non-smooth and non-convex optimisation has many applications in industry and science. One of the powerful methods in non-smooth optimisation is a bundle method. This project will develop new versions of the bundle method by using continuous approximations to the sub-differential and extend this method for solving non-convex (smooth and non-smooth) optimisation problems by using max-min of linear ....Approximate bundle methods in nonsmooth optimisation and their applications in some complex systems. Non-smooth and non-convex optimisation has many applications in industry and science. One of the powerful methods in non-smooth optimisation is a bundle method. This project will develop new versions of the bundle method by using continuous approximations to the sub-differential and extend this method for solving non-convex (smooth and non-smooth) optimisation problems by using max-min of linear functions for the approximation of the functions involved. The outcome will be a new class of effective readily implementable algorithms for the minimization of non-smooth and non-convex functions, whose usefulness will be demonstrated by applications in cluster analysis, biochemistry and robotics.
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Stationarity and regularity in variational analysis with applications to optimization. This project will significantly develop the theoretical basis of variational analysis and optimization. Improving the understanding of regularity and stationarity issues in optimization theory will lead to major national benefits in increasing efficiencies and reducing costs in many fields of human endeavour on a national and international level.
Filled function methods for global optimization and their applications. Many real problems in science, commerce and industry are restricted in the way that they are modelled and solved by the known inability to deal with global optimization problems. The development of computational efficient global optimization methods in this project will allow new more complete approaches to these problems, especially in new areas of bio-informatics, data mining, economic modelling, supply chain management, ....Filled function methods for global optimization and their applications. Many real problems in science, commerce and industry are restricted in the way that they are modelled and solved by the known inability to deal with global optimization problems. The development of computational efficient global optimization methods in this project will allow new more complete approaches to these problems, especially in new areas of bio-informatics, data mining, economic modelling, supply chain management, air traffic management, biochemical engineering and automotive industry, consequently helping Australia advance in these various areas. It will also enhance the understanding of global optimization from both theoretical and numerical viewpoints, particularly boosting optimization research in Australia.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE210101056
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explain ....Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explaining the power and limitations of these methods when compared with existing approaches. Possible benefits include safer and more reliable complex engineered systems, such as the power grid or interacting autonomous vehicles, verified by methods built on those developed in the project.Read moreRead less
An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.Read moreRead less