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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Discovery Early Career Researcher Award - Grant ID: DE200100063
Funder
Australian Research Council
Funding Amount
$394,398.00
Summary
Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the m ....Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the mathematical theory required to rigorously justify the use of such algorithms and thereby ensure the integrity of the decision tools they produce. This mathematical framework is also expected to produce new algorithms for optimisation which benefit consumers of data science such as the health-care and cybersecurity sectors.Read moreRead less
Realising the promise of neural networks for practical optimisation: improving their efficiency and effectivess through chaotic dynamics and hardware implementation. Combinatorial optimisation problems such as transportation routing and assembly-line scheduling are critical to the efficiency of many industries, but their combinatorial explosion makes rapid solution difficult. Neural networks (NNs) hold much potential for rapid solution though hardware implementation, but we need to improve the q ....Realising the promise of neural networks for practical optimisation: improving their efficiency and effectivess through chaotic dynamics and hardware implementation. Combinatorial optimisation problems such as transportation routing and assembly-line scheduling are critical to the efficiency of many industries, but their combinatorial explosion makes rapid solution difficult. Neural networks (NNs) hold much potential for rapid solution though hardware implementation, but we need to improve the quality of their solutions before developing hardware. We have previously shown that the rich dynamics of chaos can improve the efficiency and effectiveness of NNs. We aim to develop new chaotic NN models, rigorously evaluate them on industrially significant problems such as those arising in manufacturing, logistics and telecommunications, and demonstrate their speed through hardware acceleration.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.
Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowl ....Beyond black-box models: interaction in eXplainable Artificial Intelligence. This project addresses a key issue in automated decision making: explaining how a decision was reached by a computer system to its users. Its aim is to progress towards a new generation of explainable decision models, which would match the performance of current black-box systems while at the same time allow for transparency and detailed interpretation of the underlying logic. This project expects to generate new knowledge in modelling interdependencies of decision criteria using recent advances in the theory of capacities. The expected outcomes are sophisticated but tractable models in which mutual dependencies of decision rules and criteria are treated explicitly and can be thoroughly evaluated. Read moreRead less
Information Geometry and Compressive Sensing for Radar and Communications. Australia's vast distances, thin population and extensive sea approaches force us to place heavy reliance on telecommunications and the remote sensing that radar and other modalities can provide. This project will enchance capabilities in sensing to provide more reliable, robust and cost effective communications and surveillance over a wide area.
Optimal design of controlled aerodynamic bodies: from concept to prototype. This interdisciplinary project will deliver technological advances in the areas of fluid dynamics, control systems and optimisation. It utilises advanced knowledge in these areas to design manoeuvrable aerodynamic bodies and will have a direct effect on Australian defence capability.
Robust Optimal Asset Liability Management via Stochastic Control Theory. The Australian federal and state governments are strongly exposed to the Australian and international investment markets, either directly or through entities such as the Future Fund, state-owned insurers and superannuation schemes. Additionally, the investment pool represented by individual Australian's superannuation savings managed by non-government organisations is significant. Robust and effective management of these ....Robust Optimal Asset Liability Management via Stochastic Control Theory. The Australian federal and state governments are strongly exposed to the Australian and international investment markets, either directly or through entities such as the Future Fund, state-owned insurers and superannuation schemes. Additionally, the investment pool represented by individual Australian's superannuation savings managed by non-government organisations is significant. Robust and effective management of these assets in order to meet future liabilities of these funds are essential to a stable Australian economy. This research has the potential to be a key component of reliable investment management, helping make Australia an important investment hub.Read moreRead less
Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optim ....Control of Markov jumping processes with constraints. The project outcomes will constitute the set of tools for modelling and optimisation of complex stochastic systems and will lead to new and more precise characterisations of optimal behaviour of complex controllable systems arising in Resource Management, Engineering and Telecommunications. Therefore, the project fits to the research priority areas Breakthrough Science and Frontier Technologies in the topic of mathematical modelling and optimisation of Complex Systems.Read moreRead less