Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0346878
Funder
Australian Research Council
Funding Amount
$190,000.00
Summary
GeoWulf: An Inference Engine for Complex Earth Systems. The project is to build a `Beowulf' cluster as a platform for solving
complex data inference problems in the Earth sciences, and in
particular the fields of thermochronology, seismology, crustal and
mantle dynamics, and landform evolution. A Beowulf cluster is a
network-linked set of commonly available `off-the-shelf' PC-computers
configured to give unprecedented performance/cost ratio. Projects
using the Beowulf facility will combine ....GeoWulf: An Inference Engine for Complex Earth Systems. The project is to build a `Beowulf' cluster as a platform for solving
complex data inference problems in the Earth sciences, and in
particular the fields of thermochronology, seismology, crustal and
mantle dynamics, and landform evolution. A Beowulf cluster is a
network-linked set of commonly available `off-the-shelf' PC-computers
configured to give unprecedented performance/cost ratio. Projects
using the Beowulf facility will combine state-of-the-art computational
techniques recently developed at ANU, and high quality data sets
collected over the past decade to address fundamental questions in
the Geosciences.Read moreRead less
Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk ....Frontiers in inference about risk. The project aims to develop new methods for robust risk evaluation and minimisation under various constraints and scenarios. Risk evaluation, estimation and prediction using past data is a central activity in diverse areas such as finance, insurance, superannuation and environmental regulation. The project aims to propose and solve innovatively robust risk optimisation problems under constraints, taking into account the time dynamics. Applications include risk management around natural catastrophes and long-term asset investment of pension funds. The solutions and outcomes are expected to deliver optimal resource allocation proposals and better management of risk exposure in practice.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE240100006
Funder
Australian Research Council
Funding Amount
$444,847.00
Summary
Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techn ....Robust Derivative-Free Algorithms for Complex Optimisation Problems. Mathematical optimisation gives a systematic way for optimal decision-making. This project aims to develop new mathematical tools for complex optimisation problems where limited problem information is available. It will generate new foundational theories for alternative optimisation tools, introducing substantial new capability and rigour to the discipline. The project will create significant new mathematical optimisation techniques and create world-leading and publicly available software. These new techniques and software may ultimately be able to solve some of the most complex optimisation problems in research and industry, such as improving long-term climate predictions and designing 3D-printed medical implants.Read moreRead less
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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New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software ....New Theory and Algorithms for Nonsmooth Optimisation with Application to Integer Programming. Mathematical optimisation plays a key role in a wide variety of applications in business, industry, engineering and science. For example, airlines cannot fly and radiation treatment for cancer cannot be delivered without solving (a series of) optimisation problems. Some classes of optimisation problem are very well solved, with clear mathematical foundations, efficient algorithms, and reliable software implementations. Both nonsmooth and integer optimisation problems have a good mathematical basis, but there are "gaps"; existing methods cannot always solve real industrial problems. This project will deliver better methods, built on better theory, and so will yield better solutions for important applications.Read moreRead less
Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of poi ....Approximation, Cubature and Point Designs on Spheres. The sphere is important in fields ranging from geophysics to global climate modelling to chemistry to codes for modern communications. This project aims to strengthen and unify key areas of mathematics on the sphere and at the same time provide methods and constructiions of practical significance. The areas of focus are constructive approximation of functions on the sphere, numerical integration on the sphere, and well distributed sets of points on the sphere, including spherical designs.Read moreRead less