Course Information

Lecturer:

Dr. Michelle Dunbar, The University of Sydney

Synopsis:

In many real-world problems, we wish to seek the best possible solution under a given set of constraints. How do we achieve this? The answer is optimisation! In this course we will investigate the art of translating real-world problems into mathematics, and develop the mathematical tools and techniques to solve these problems efficiently in practice. The course will investigate both theory and practical aspects, and will cover different real world examples from medicine and industry.

Course Overview:

  • Linear Programming (formulations, graphical solutions)
  • The Simplex Method for Solving Linear Programs
  • Duality
  • Network Optimisation (link and path flow formulations for networks)
  • Shortest-Path Algorithms
  • Integer Programming (formulations)
  • Introduction to Non-Linear optimisation
  • Real-World Applications

Contact Hours:

28 hours, made up of 10 two-hour lectures and 8 tutorial/lab sessions.

Timetable:

Please see the Timetable for scheduled class times during the AMSI Summer School 2017.
Please note: Optimisation is held concurrently with Computational Bayesian Statistics and students cannot attend both courses in 2017.

Prerequisites:

  • Multivariable calculus
  • Linear Algebra
  • Introductory knowledge of a programming language (Matlab preferred). There will however be a refresher and necessary instruction provided as part of the course.

Assessment:

  • Two written assignments: 20% each
  • Final examination: 60%

Resources:

Course material will be self-contained; however you might find the following supplementary texts helpful for further reading.

  • Bertsimas, J. N. Tsitsiklis, “Introduction to Linear Optimization”, 1997.
  • Winston, “Operations Research: Applications and Algorithms”, 2004.
  • A. Wolsey, “Integer Programming”, 1998
  • S. Bazaraa, H. D. Sherali, C. M. Shetty, “Nonlinear Programming : Theory and Algorithms”, 2006
  • Introduction to Matlab (provided by lecturer)

Lecturer Biography

Optimisation

Dr. Michelle Dunbar, The University of Sydney

Michelle completed her PhD in Applied Mathematics at the University of New South Wales in 2012, and from 2012-2015 was a Vice Chancellor’s Postdoctoral Research Fellow in the SMART Infrastructure Facility at the University of Wollongong.

Michelle has experience in applying mathematical optimisation techniques to both medicine and public transport networks, to assist in key operational decisions and provide robust solutions under uncertainty. She also has experience in applying non-linear optimisation tools to a variety of medical datasets to allow for improved disease detection and diagnosis; one of these tools has subsequently been taken up by a health care company.

Michelle is currently a postdoctoral fellow in the Sydney Medical School and is involved in developing optimisation tools to enhance medical imaging and treatment for cancer patients.

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