Discovery Early Career Researcher Award - Grant ID: DE170100234
Funder
Australian Research Council
Funding Amount
$360,000.00
Summary
Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation ....Exact and hybrid algorithms for the Aircraft Landing Problem. This project aims to develop algorithms with superior guaranteed performance. Aircraft Landing Problems (ALP) are an important class of decision problems. Optimal solution of an ALP is applicable in transportation and health care delivery, benefitting systems experiencing long delays. This project aims to address several of the Australian Government's Science and Research Priorities, focusing on food supply chains, effective operation and resource allocation in transport, and better models of health care delivery and services.Read moreRead less
COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet i ....COMPLEX NETWORKS: DYNAMICS, OPTIMIZATION AND CONTROL. Complex networks such large power grids, the Internet, transportation networks and co-operation networks of all kinds provide challenges for frontier technologies particularly computing, communication and control. In particular, advanced societies have become dependent on large infrastructure networks to an extent beyond our capability to plan and control them. The recent spate of collapses in power grids and virus attacks on the Internet illustrate the need for research on modelling, analysis of behaviour, planning and control in such networks. This project aims to establish research in this area for Australia's benefit.Read moreRead less
Dynamics and Security Control of Complex Networks. The research will yield basic techniques to analyse, design and operate complex networks so that security, as well as performance, is achieved. These techniques will be further developed towards particular applications including power grids and telecommunication networks. However, the emphasis is on providing basic ideas and techniques.
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
Construction of near optimal oscillatory regimes in singularly perturbed control systems via solutions of Hamilton-Jacobi-Bellman inequalities. Problems of optimal control of systems evolving in multiple time scales arise in a great variety of applications (from diet to environmental modelling). This project addresses the challenge of analytically and numerically constructing rapidly oscillating controls that would 'near optimally coordinate' the slow and fast dynamics.
Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the interna ....Topological data analysis for enhanced modelling of the physical properties of complex micro-structured materials. The way water flows through sandstone depends on the connectivity of its pores, the balance of forces in a grain silo on the contacts between individual grains, and the impact resistance of metal foam in a car door on the arrangement of its cells. These structural properties are described mathematically by topology. Advanced three-dimensional X-ray imaging can now reveal the internal detail of micro-structured materials. Recent developments in image analysis mean it is possible to compute accurate topological information from such images. This project aims to investigate how fundamental measures of shape influence the physical properties of complex materials and clarifies the mathematics that underpins these relationships.Read moreRead less
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Novel techniques for statistical and mathematical analyses of sequence data. Algorithms will be developed for analysing and comparing the sequences of DNA letters and amino acids constantly being generated in massive quantities by biological research. The novel approach taken is based on the statistical frequency of occurrence of short words and is designed specifically for situations where current methods fail.
Occupational measures, perturbations and complex deterministic systems. When tackling complex problems, scientists and engineers seek methods that judiciously exploit stochasticity and perturbations as antidotes to unpredictability of outputs that the latter can induce if they inadvertently influence their models. The project proposes for this study vaccine-like perspective of stochasticity and singular perturbations.
Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advan ....Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice. Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.Read moreRead less