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
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