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
Discovery Early Career Researcher Award - Grant ID: DE210101056
Funder
Australian Research Council
Funding Amount
$395,775.00
Summary
Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explain ....Realising the potential of hyperbolic programming. This project aims to develop and analyse new mathematical and algorithmic methods for polynomial optimisation and decision problems. In doing so it expects to generate knowledge and tools in mathematical optimisation that build on recent developments in the theory of hyperbolic polynomials. Expected outcomes include more scalable and/or reliable methods for polynomial optimisation and safety verification of dynamical systems, and theory explaining the power and limitations of these methods when compared with existing approaches. Possible benefits include safer and more reliable complex engineered systems, such as the power grid or interacting autonomous vehicles, verified by methods built on those developed in the project.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
Discovery Early Career Researcher Award - Grant ID: DE240100042
Funder
Australian Research Council
Funding Amount
$339,237.00
Summary
Hybrid optimisation for coordinating autonomous trucks and drones. This project aims to build analytics for controlling a fleet of autonomous trucks and drones working in tandem to deliver retail goods and disaster relief. This project expects to develop new mathematical and artificial intelligence algorithms for routing and scheduling the vehicles and for directing the multi-modal transfer of goods between vehicles in real-time as traffic conditions change. Expected outcomes of this project inc ....Hybrid optimisation for coordinating autonomous trucks and drones. This project aims to build analytics for controlling a fleet of autonomous trucks and drones working in tandem to deliver retail goods and disaster relief. This project expects to develop new mathematical and artificial intelligence algorithms for routing and scheduling the vehicles and for directing the multi-modal transfer of goods between vehicles in real-time as traffic conditions change. Expected outcomes of this project include new theories and technologies that enable a central computer to remotely control the autonomous fleet for maximum efficiency. Benefits in transport and logistics include improved freight productivity through reducing costs and delivery times.Read moreRead less
Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the developme ....Large scale nonsmooth, nonconvex optimisation. This project aims to develop, analyse, test and apply (sub) gradient-based methods for solving large scale nonsmooth, nonconvex optimisation problems. Large scale problems with complex nonconvex objective and/or constraint functions are among the most difficult in optimisation. This project will generate new knowledge in numerical optimisation and machine learning. The use of structures and sparsity of large scale problems will lead to the development of better models, and more accurate and robust methods. The expected outcomes of the project are ready-to-implement and apply numerical methods for solving large-scale, nonsmooth, nonconvex optimisation problems, as well as problems in machine learning and regression analysis.Read moreRead less
Industrial Transformation Training Centres - Grant ID: IC200100009
Funder
Australian Research Council
Funding Amount
$4,861,236.00
Summary
ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdiscip ....ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA). OPTIMA addresses industry’s urgent need for decision-making tools for global competitiveness: reducing lead times, and financial and environmental costs, while improving efficiency, quality, and agility. Despite strong expertise in academia, industry is yet to fully benefit from optimisation technology due to its high barrier to entry. Connecting industry partners with world-leading interdisciplinary researchers and talented students, OPTIMA will advance an industry-ready optimisation toolkit, while training a new generation of industry practitioners and over 120 young researchers, vanguarding a highly skilled workforce of change agents for transformation of the advanced manufacturing, energy resources, and critical infrastructure sectors.Read moreRead less