Optimisation research

Optimisation has been one of the most active domains of modern mathematical research for over a century.

Mission and vision

Optimisation encompasses a broad panorama of research agendas from the foundations of modern mathematical analysis and computation, to development of modelling and numerical optimisation tools used within industry today to solve challenging large scale problems with speed and reliability. Modern computational tools require fundamental theoretical developments both of a mathematical nature and from an algorithmic and complexity view point. Optimisation bridges applied mathematics, modelling and computing science.

Optimisation research is engaged in the development of fundamental mathematical theory for the creation of new optimisation techniques for the solution of challenging optimisation problems. We are actively engaged in the international efforts directed at the solution of fundamental challenges faced by the optimisation community. We are also committed to the promotion and dissemination of new knowledge via engagement with the local Australian mathematical community and the promotion of collaborations with industry and government organisations.

The members of our optimisation research actively collaborate with other Australian research centres focussed on optimisation and computation, in particular CARMA at the University of Newcastle and CIAO at Federation University Australia. We also have extended overseas collaborations, in particular in the US and in Europe.

RMIT Optimisation holds weekly research meetings (with connection available to external participants via Visimeet). We also organise optimisation workshops and post all materials related to the meetings.

Overview

A mathematical optimisation problem seeks feasible values for a set of decision variables, i.e. seeks to make decisions that satisfy a given set of constraints representing the feasibility of decisions as subject to real world factors, so as to either maximize or minimize a function of these variables which is known as the objective function (this measures the value we place on a set of decisions). An enormous range of practical problems can be formulated in these terms, ranging from the design of optimal controllers in engineering, to delivery of cancer radiation treatment, to extraction of the greatest value from open-pit mines, to best environmental management practices, football pools, efficient management of regional air traffic, resource allocation or project management and scheduling.

Advances in algorithms and optimisation technology resulting from mathematical research, and from closely related branches of computer science, have led to a revolution in the business world, with optimisation-based decision support tools now pervasive in large, complex organizations, and critical to their planning and operational activities. An indication of the significance of this development can readily be found in INFORMS, SIAM and the Optimisation Society publications. Mathematical optimisation has also expanded rapidly in recent years into new areas of science, medicine and engineering. Areas such as computational biology, renewable energy and the management of electricity networks, infrastructure security, are just a few of the frontier application areas driving exciting new developments.

Areas of specialisation

  • Nonsmooth/Variational analysis: An extension of classical analysis to support optimisation in an essentially nonsmooth setting. In other words, this branch of mathematics deals with optimisation problems where the defining constraints or objective function has jumps in their values of rates of change.
  • Convex analysis: Deals with the special structure engendered to an optimisation problem within which the constraints and objective functions are geometrically rotund. This enables special analysis and efficient algorithms.
  • Conic optimisation: The study of optimisation problems with conic constraints where the cones have special structural properties (such as linear, semidefinite and hyperbolic programming).
  • Game theory: Mathematical framework to study decision making problems in the presence of conflicting interests.
  • Stochastic optimisation / Online optimisation: The study of decision making problems where decisions have to be made based on incomplete information about future events. In the former case the possible futures are associated with a probability distribution and one seeks to optimise an expectation value while in the latter information arrive over the time and one seeks to optimise in the worst case.
  • Dynamical systems and optimal control: The study of systems that evolve in time whose evolution can be influenced by the choice of input parameters, in order to optimise their performance.
  • Combinatorial optimisation, networks and graphs: Optimisation of problems in which some or all of the variables take discrete values, or when the problem's structure exhibits discrete characteristics. Graphs are such particular discrete structures.
  • Algorithm efficiency/ Complexity theory / Polynomial approximation: Theoretical analysis of the performance of numerical algorithms that allows to measure the efficiency of the methods - theoretical analysis of the best possible performance of any algorithm for a problem that allows to characterise the hardness of a problem – design and analysis of algorithms with performance guarantees.
  • Modelling and solving real problems: Using optimisation models for addressing real problems and challenges for the society: the group is involved in various domains of applications like environmental management, energy and natural resources management and emergency management.

Members

RMIT staff

  • Babak Abbasi 
  • Serdar Boztas
  • Brian Dandurand
  • Marc Demange
  • Andrew Eberhard
  • Robin Hill
  • John Hearne
  • Yanqun Liu
  • Yousong Luo
  • Bill Moran
  • Melih Ozlen
  • Vera Roshchina 
  • Sergei Schreider
  • Cerasela Tanasescu
  • Robert Wenczel

RMIT HDR students

  • Nigel Clay
  • Corrie Jacobien Carstens
  • Jeffrey Christiansen
  • David Ellison
  • Cameron MacRae
  • Leo Shuai
  • Tian Sang

External members

  • Alexander Kruger (Federation University Australia)
  • Nadezda Sukhorukova (Swinburne University of Technology)
  • Julien Ugon (Federation University Australia)

Undertake a research degree

Prospective Higher Degree by Research applicants should contact one of our academic or post-doc members to discuss supervision of a research project.

Related research degrees

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Acknowledgement of country

RMIT University acknowledges the people of the Woi wurrung and Boon wurrung language groups of the eastern Kulin Nations on whose unceded lands we conduct the business of the University. RMIT University respectfully acknowledges their Ancestors and Elders, past and present. RMIT also acknowledges the Traditional Custodians and their Ancestors of the lands and waters across Australia where we conduct our business.

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