Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with inter ....Constrained and Stable Solutions of Nonlinear and Semismooth Equations. In this project, comprehensive models for designing safe power system parameters will be proposed, efficient algorthms for solving these models will be constructed. The new models and algorithms in this project will provide efficient tools to prevent catastrophic events in power systems, which is related with national security. This project will also strengthen collaboration of Australian applied
mathematians with international researchers and engineering scientists. This is important for the advance of science and technology in
Australia.Read moreRead less
An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, mos ....An optimisation-based framework for non-classical Chebyshev approximation. This project aims to solve open mathematical problems in multivariate and piecewise polynomial approximations, two directions that correspond to fundamental obstacles to extending classical approximation results. Through an innovative combination of optimisation and algebraic technique, the project intends to develop foundations for new results in approximation theory, and new insights into other areas of mathematics, most notably optimisation. The techniques and methods developed should also have significant benefits in the many disciplines where approximation problems appear, such as engineering, physics or data mining. The research outputs resulting from this project will be used in a wide range of fields to help implement programs, policies and improve decision making.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.
Optimising experimental design for robust product development: a case study for high-efficiency energy generation. This project tackles key mathematical challenges to provide a powerful new methodology and tool for optimal product design, making smarter use of limited information, minimising costly trials, shortening the product cycle, and boosting the competitiveness of both the Australian manufacturing and alternative energy production industries.