| Project ID |
Investigator(s) |
Summary |
Administering Organisation |
| DP160101537 |
Professor Jonathan Borwein; Dr Jeffrey Hogan; Professor Dr Russell Luke |
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. |
The University of Newcastle |
| DP160100746 |
Professor Paul Cally; Professor Hans De Sterck; Dr Sergiy Shelyag |
This project aims to develop numerical methods for complex magnetohydrodynamic simulations able to handle sharp and dynamically evolving inhomogeneities, spherical geometries, and dramatic variations in density and wave speed across the simulation domain. The project plans to develop these methods within the context of solar wave processes, which are fundamental to the transfer of energy from the sun’s interior to its outer atmosphere, to the acceleration of the solar wind that rushes past the Earth continually, and to solar activity in general. This would provide the best available modelling of how the sun’s atmosphere works, with direct implications for how the Earth’s space environment is determined by solar storms and eruptions. |
Monash University |
| DP160100854 |
Associate Professor AlexanderKruger; Professor Jiri Outrata; Professor Michel Théra; Professor Dr Marco López Cerdá; Professor Assen Dontchev; Dr Rene Henrion |
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. |
Federation University Australia |
| DP160102819 |
Professor Jie Sun; Dr Honglei Xu; Eminent Professor Ralph Rockafellar |
This project seeks to develop theory and methodology in optimisation which take advantage of recent progress in understanding and treating risk in decision making. Problems of optimisation in the face of uncertainty must confront the risk inherent in having to make reliable decisions before knowing the outcomes of crucial random variables on which costs and constraints may depend. Recent theoretical developments, featuring ‘measures of risk’ beyond just-expected values and quantiles offer hope of major new advances. This project aims to achieve such advances not only in optimisation but also in models of equilibrium that likewise have to deal with uncertainty. Extending current theory and methodology to such multi-stage stochastic models is a challenge. Besides taking up this challenge for its own sake, a major goal of this research will be to use the results in solution algorithms. |
Curtin University of Technology |
| DP160100639 |
Professor Doreen Thomas; Associate Professor Marcus Brazil; Dr Charl Ras; Professor Dr Martin Zachariasen |
The goal of this project is to construct a mathematical framework for the design of minimum-cost networks that are robust and avoid obstacles. Physical networks such as those required for communication, power and transportation are vital for our society, but are costly from economic and environmental viewpoints. There is a need for mathematical optimisation tools to design minimum-cost networks that take into account practical considerations such as surviving local connectivity failures and avoiding pre-existing obstacles. These are recognised as mathematically challenging problems. Current approaches employ restrictive models that do not capture the flexibility of modern infrastructure networks. This project aims to develop geometric design methods using variable ‘Steiner points’, leading to fast algorithms for optimally solving these problems. |
The University of Melbourne |
| DP160101755 |
Associate Professor Thanh Tran; Professor Beniamin Goldys; Professor Zdzislaw Brzezniak; Professor Dr Andreas Prohl; Professor Dr Ernst Stephan; Associate Professor Salim Meddahi |
This project aims to develop novel mathematical theories and numerical methods for problems affected by uncertainty in input data. This type of uncertainty exists in most mathematical models of real life applications. For these problems, a single deterministic simulation with one set of input data is of limited use. Therefore, novel techniques to deal with randomness are essential. The problems in this project are driven by specific applications from ferromagnetism, structural acoustics and vibration. The new theories may lay the foundation for understanding ferromagnetic materials and structural acoustics. The novel approaches to be developed in this project may form the basis for the study of stochastic liquid crystal theory and other interface problems. |
The University of New South Wales |
