Discovery Early Career Researcher Award - Grant ID: DE150101137
Funder
Australian Research Council
Funding Amount
$312,000.00
Summary
Two-scale numerical modelling of coupled transport in heterogeneous media. Groundwater constitutes a vital part of water resources in Australia, however, the quality of this water is susceptible to contamination. This project aims to develop an innovative two-scale mathematical model for contaminant transport that accounts for small-scale heterogeneities found in the unsaturated zone of an aquifer located between the ground surface and the underlying groundwater. The project aims to develop valu ....Two-scale numerical modelling of coupled transport in heterogeneous media. Groundwater constitutes a vital part of water resources in Australia, however, the quality of this water is susceptible to contamination. This project aims to develop an innovative two-scale mathematical model for contaminant transport that accounts for small-scale heterogeneities found in the unsaturated zone of an aquifer located between the ground surface and the underlying groundwater. The project aims to develop valuable environmental insights, a simulation tool that will help in making decisions regarding the future management of Australian groundwater resources, and a general two-scale modelling and simulation framework for other important environmental and industrial problems involving coupled transport in heterogeneous media.Read moreRead less
Effective computational methods for nonlinear cone optimisation with industrial applications. This project brings together a number of national and international researchers whose combined expertise will focus on solving optimisation problems arising in a range of industries. The work will result in new cutting edge optimisation technology that can benefit industry and the community.
Discovery Early Career Researcher Award - Grant ID: DE180100923
Funder
Australian Research Council
Funding Amount
$348,575.00
Summary
Efficient second-order optimisation algorithms for learning from big data. This project aims to apply a diverse range of scientific computing techniques to design and implement new, second-order methods that can surpass first-order alternatives in the next generation of optimisation methods for large-scale machine learning (ML). Scalable optimisation methods are now an integral part ML in the presence of “big data”. While the development of efficient first-order methods has grown in the ML comm ....Efficient second-order optimisation algorithms for learning from big data. This project aims to apply a diverse range of scientific computing techniques to design and implement new, second-order methods that can surpass first-order alternatives in the next generation of optimisation methods for large-scale machine learning (ML). Scalable optimisation methods are now an integral part ML in the presence of “big data”. While the development of efficient first-order methods has grown in the ML community, second-order alternatives have largely been ignored. The project expects to facilitate the development of more effective ML algorithms for extraction of knowledge from large data sets.Read moreRead less
Robust numerical solution of partial differential equations on petascale computer systems with applications to tsunami modelling and plasma physics. The project will apply new mathematical ideas to exploit the unprecedented computational resources provided by the next generation of high performance computers. The resulting techniques and software will form a key component for the science needed to understand the workings of complex dynamical systems, such as tsunamis and fusion reactors.
Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, ....Robust Reformulation Methods. Many decision problems in engineering, business and economics are modeled as nonlinear continuous optimization problems. Often these are made difficult by the existence of constraints. In this project, we reformulate such problems as constrained nonsmooth equations, rather than optimization problems, and develop generalized Newton and quasi-Newton methods for solving them. The expected outcomes of this project include a systematic theory of reformulation methods, and robust and efficient algorithms for solving some important nonlinear continuous optimization problems. There is high potential for applications in engineering, business and finance.Read moreRead less
Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an inte ....Quadratic Support Function Technique to Solving Hard Global Nonconvex Optimization Problems. Optimization techniques are becoming increasingly beneficial to modern Australian society in areas such as manufacturing and commerce by improving technical and management decisions. The proposed research is expected to produce enhanced optimization techniques that can be applied to solve a wider range of important problems too complex to be currently solved. The proposed research also represents an international collaboration which will improve Australia's ability to participate effectively in international research and innovation and to produce globally competitive mathematical technologiesRead moreRead less
Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national be ....Continuous Optimization with Linear Matrix Inequality Constraints. The proposed research is expected to lead to new insights and new joint collaborative work for both Autralian and Korean partners. Joining forces of the two teams will ensure that a full range of techniques can be utilized to provide rapid successful research outcomes. The proposed collaboration will give better opportunity to increase the visibility of the work from Korea in Australia, and vice versa. One of the key national benefits is that the proposed research collaboration will provide extremly fertile ground for training postdoctoral researchers and graduate students in one of the most applicable areas of mathematics.Read moreRead less
Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable condition ....Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been
achieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable conditions for a global optimum is a serious limitation. This project will develop verifiable such global optimality conditions for many classes of these problems. A new methodology, functional abstract convexity, developed by CIs and has shown promising results, will be extended and applied for solving these problems.Read moreRead less
A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. ....A new improved solution to global optimization over multivariate polynomials: Mathematical principles, numerical methods and selected applications. Optimization technology is becoming increasingly beneficial to modern Australian society in areas such as wireless communications and manufacturing by improving performance or reducing costs. Our research will produce enhanced global optimization methodologies, capable of solving a wider range of problems that are currently too complex to be solved. Since global optimization technology is used in many scientific disciplines and modern industrial applications, the research will make many Australian science and industries more competitive. Our research also represents a program of high profile international collaborations that will improve Australia's ability to produce internationally competitive optimization technology.
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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