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.
Read moreRead less
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.
Read moreRead less
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
Economic Scheduling for Efficient Management of Clusters and their Cooperative Federation. Clusters of commodity computers have emerged as mainstream parallel and distributed platforms for high-performance computing. They are presented together as a single, unified resource to the end users by middleware technologies such as resource management and scheduling (RMS) systems. However, existing cluster RMS systems continue to use system centric models rather than utility models for the management a ....Economic Scheduling for Efficient Management of Clusters and their Cooperative Federation. Clusters of commodity computers have emerged as mainstream parallel and distributed platforms for high-performance computing. They are presented together as a single, unified resource to the end users by middleware technologies such as resource management and scheduling (RMS) systems. However, existing cluster RMS systems continue to use system centric models rather than utility models for the management and allocation of resources. There is also little emphasis on the construction of a cooperative federation of clusters to facilitate transparent sharing of resources. To enhance the value delivered by shared clusters, we propose the use of computational economy metaphor in resource management. This project aims to develop (A) computational economy based scheduling policies for allocation of resources and (B) a software infrastructure for creation of cooperative federation of distributed clusters.Read moreRead less
Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this ear ....Stochastic Geometry for Multi-sensor Data Fusion System. The aim of this project is to develop efficient algorithms for tracking and sensor management in a multi-sensor multi-target environment. Finite random set theory provides a natural way of representing a random number of (random) object states, an issue that has been largely ignored in the tracking literature until recently. Although a satisfactory foundation for multiple object filtering has been provided by random set theory, in this early stage no algorithm capable of tracking many targets has emerged from this framework. We are confident that efficient algorithms can be developed by exploiting the insights and mathematical tools of stochastic geometryRead moreRead less
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
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