MTH3330 Optimisation and operations research

This unit introduces some of the fundamental methods from operations research and computational mathematics for continuous optimisation problems. A range of such optimisation problems appear in economics, engineering, finance, business, data science and many other application areas. You will receive an introduction to the mathematical theory of continuous optimisation with a focus on linear programming methods and smooth non-linear programming. This will broadly include duality theory, the simplex method for linear programming, Lagrangian relaxation methods for dealing with constraints, quadratic programming, and some methods for more general non-linear problems including iterative approximation. You will learn to implement the computational methods efficiently, how to test their implementations for accuracy and performance, and to interpret the results. You will work on realistic models for applications in a variety of fields. Applications may include examples of supply chain optimisation, economic modelling (including shadow prices), product mix optimisation, portfolio optimisation, parameter estimation and machine learning.