Stability of Generalised Equations and Variational Systems. 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 expect ....Stability of Generalised Equations and Variational Systems. 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.Read moreRead less
Structured barrier and penalty functions in infinite dimensional optimisation and analysis. Very large scale tightly-constrained optimisation problems are ubiquitous and include water management, traffic flow, and imaging at telescopes and hospitals. Massively parallel computers can solve such problems and provide physically realisable solution only if subtle design issues are mastered. Resolving such issues is the goal of this project.
Low emission road transportation: harnessing the potential of alternative fuels and advanced vehicle technologies through online optimisation. This project will develop fundamental mathematical theory and use it to enable the best possible CO2 reduction capability in road vehicles. The cost of different technologies and fuels will then be compared to determine the most cost effective approaches to reduce road transport emissions.