HYBRID METHODS FOR SOLVING LARGE-SCALE OPTIMISATION PROBLEMS. Mathematical modelling and optimisation plays a crucial role in the advancement of modern business, science and technology. A significant benefit of this project is the development of a range of powerful computational tools for improving the productivity of Australian industry, including: agriculture; communications; defence; manufacturing; mining and petroleum; transport and logistics. These tools will be built upon advances in the f ....HYBRID METHODS FOR SOLVING LARGE-SCALE OPTIMISATION PROBLEMS. Mathematical modelling and optimisation plays a crucial role in the advancement of modern business, science and technology. A significant benefit of this project is the development of a range of powerful computational tools for improving the productivity of Australian industry, including: agriculture; communications; defence; manufacturing; mining and petroleum; transport and logistics. These tools will be built upon advances in the fundamental theory developed by the research team. The resulting high quality publications and associated algorithms will greatly enhance Australia's international scientific reputation and provide Australian industry with new cutting-edge optimisation technology.Read moreRead less
Robust methods for hard optimization problems. Highly advanced industrial and information-based societies depend on complex systems that underpin their infrastructure and technologies. Mathematical modelling and optimization techniques are most frequently deployed for the development and refinement of these systems. This project focuses on an important class of difficult optimization problems that arise in many applications. A significant benefit of this project is the development of a number of ....Robust methods for hard optimization problems. Highly advanced industrial and information-based societies depend on complex systems that underpin their infrastructure and technologies. Mathematical modelling and optimization techniques are most frequently deployed for the development and refinement of these systems. This project focuses on an important class of difficult optimization problems that arise in many applications. A significant benefit of this project is the development of a number of robust methods for these hard optimization problems. These methods will be built upon advances in the fundamental theory developed by the research team. The resulting high quality publications and associated algorithms will greatly enhance Australia's international scientific reputation.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.
Read moreRead less
Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science ....Advanced computational algorithms for three-dimensional systems. This project deals with the development, analysis and implementation of efficient computer algorithms for a range of complex three dimensional systems. Major areas of focus are forward and inverse acoustic and electromagnetic scattering; dynamical and evolution processes in water waves and tumour growth; and the solution of mathematical models on spheres (earth). Potential application areas of the project include defence science; ocean engineering; medical research; meteorology and global environmental sciences.Read moreRead less
Mathematics in the round - the challenge of computational analysis on spheres. Real world problems formulated on spheres (including physical problems for the whole earth) provide many difficult challenges. This project aims at developing algorithms to solve problems on spheres in two and higher dimensions, with applications ranging from geophysics to signal analysis.
Application of Optimisation Techniques to the Truck/Loader Selection Problem in Mining. Australia has world class deposits of most major mineral commodities and is a major producer and exporter of coal and many metals. The mining industry has an annual turnover of around $40 billion. A significant component (up to 55%) of mining costs is material handling. This project aims to develop computational tools for determining the best selection of trucks and loaders for the mining operation. To da ....Application of Optimisation Techniques to the Truck/Loader Selection Problem in Mining. Australia has world class deposits of most major mineral commodities and is a major producer and exporter of coal and many metals. The mining industry has an annual turnover of around $40 billion. A significant component (up to 55%) of mining costs is material handling. This project aims to develop computational tools for determining the best selection of trucks and loaders for the mining operation. To date this important problem has not been addressed. Our strategy is to develop accurate mathematical models and cutting edge optimisation techniques for their solution. The research outcomes will have significant outcomes for the mining industry.Read moreRead less