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.
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
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
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