Geometry in projection methods and fixed-point theory. This project aims to resolve mathematical challenges arising from problems with specific structure typical for key modern applications, such as big data optimisation, chemical engineering and medical imaging. We focus on developing new mathematical tools for the analysis of projection methods and accompanying fixed point theory, specifically targeting the refinement of the geometric intuition for algorithm design techniques to inform the imp ....Geometry in projection methods and fixed-point theory. This project aims to resolve mathematical challenges arising from problems with specific structure typical for key modern applications, such as big data optimisation, chemical engineering and medical imaging. We focus on developing new mathematical tools for the analysis of projection methods and accompanying fixed point theory, specifically targeting the refinement of the geometric intuition for algorithm design techniques to inform the implementation of optimal methods for huge-scale optimisation problems.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
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
Scaling Disk-Resident Learned Indexes For Database Systems. This project aims to investigate new disk-resident learned indexing algorithms to store and process data in database systems by advancing the state-of-the-art in memory-resident learned modeling. This project expects to generate new knowledge in the area of digital storage technologies utilising novel and efficient techniques in learned indexing for big data. This should provide significant benefits to enable modern database systems to ....Scaling Disk-Resident Learned Indexes For Database Systems. This project aims to investigate new disk-resident learned indexing algorithms to store and process data in database systems by advancing the state-of-the-art in memory-resident learned modeling. This project expects to generate new knowledge in the area of digital storage technologies utilising novel and efficient techniques in learned indexing for big data. This should provide significant benefits to enable modern database systems to scale with the massive growth of data, improve the efficiency of data processing, improve the effectiveness of projects that utilise big data, and dramatically reduce energy costs in Australian data centres when storing and retrieving data from databases and lower their carbon footprints.Read moreRead less
Beyond Query: Exploratory Subgraph Discovery and Search System. Exploring co-working user groups in dynamic network data is a vital challenge in many applications, for example, in online education. This project aims to discover new relationships of users and compute their co-working performance in continuous time periods. The outcomes of the project are to design effective subgraph exploratory models, three novel types of subgraph search solutions, and devise a friendly exploratory subgraph sear ....Beyond Query: Exploratory Subgraph Discovery and Search System. Exploring co-working user groups in dynamic network data is a vital challenge in many applications, for example, in online education. This project aims to discover new relationships of users and compute their co-working performance in continuous time periods. The outcomes of the project are to design effective subgraph exploratory models, three novel types of subgraph search solutions, and devise a friendly exploratory subgraph search system for supporting the real-time network data analytics. The success of the project will make a significant contribution to the scientific foundation of graph data mining and its applications in data engineering domains, as well as benefiting co-working performance of people in Australian labor markets.Read moreRead less
Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the developme ....Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the development of better models, and more accurate and robust methods. The expected outcomes of the project are ready-to-implement and apply numerical methods for solving large-scale, nonsmooth, nonconvex optimisation problems, as well as problems in machine learning and regression analysis.Read moreRead less
Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
Real-time global optimisation for distributed parameter control systems. This project aims to develop real-time optimal control algorithms for distributed parameter systems involving both time and spatial variables and multiple time-delays, with a focus on mining and energy applications. Current optimal control algorithms for such systems are too slow for real-time use and often get trapped at local optima, which can be vastly inferior to the global solution. This project will result in a new op ....Real-time global optimisation for distributed parameter control systems. This project aims to develop real-time optimal control algorithms for distributed parameter systems involving both time and spatial variables and multiple time-delays, with a focus on mining and energy applications. Current optimal control algorithms for such systems are too slow for real-time use and often get trapped at local optima, which can be vastly inferior to the global solution. This project will result in a new optimal control framework, underpinned by recent advances in constraint propagation, switching surface optimisation, and input regularisation. It will result in cutting-edge mathematical tools to complement and exploit new technologies and optimise key processes in natural gas liquefaction and zinc and alumina production, increasing efficiency and reducing the ecological footprint. This project will lead to new cutting-edge control algorithms for replacing the inefficient manual operations endemic in Australia’s natural gas and mineral processing plants.Read moreRead less
Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expect ....Stability of Generalised Equations and Variational Systems. This project seeks to advance a new mathematical theory of variational analysis which may lead to applications in optimisation. The emphasis will be on extensions of regularity concepts appropriate for studying stability (the ‘radius of good behaviour’) of solutions to optimisation problems, particularly those of semi-infinite optimisation and programs with equilibrium constraints, when standard assumptions are not satisfied. The expected outcomes may have an impact in enhancing the convergence of numerical methods and facilitating the post-optimal analysis of solutions. It may also generate new tools for increasing efficiencies and cost reductions in engineering, logistics, economics, financial systems, and environmental science.Read moreRead less
Relaxed reflection methods for feasibility and matrix completion problems. The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in ....Relaxed reflection methods for feasibility and matrix completion problems. The project proposes to further develop the non-linear convergence theory, and to provide problem-specific implementations. Many applied and pure problems require solution of a large set of linear or nonlinear equations (or inequalities). Highly effective, parallelisable methods are based on iterated projection or reflection algorithms which aggregate information about individual equations. The theory is well developed in the linear case, but does not explain many important applications for which they are often highly successful (eg optical aberration correction, protein reconstruction, tomography, compressed sensing). The project also plans to provide heuristics to help explain why an algorithm performs well on one class of applications but fails on another.Read moreRead less