Optimisation and numerical methods for engineers

This unit will introduce fundamental methods and concepts from numerical linear algebra and optimisation, and show how they apply to a range of engineering problems. A focus of the unit will be on the interplay between a problem's mathematical properties and the selection and performance of reliable computational methods to solve that problem. Applications will be drawn from a range of engineering contexts such as electrical circuits, dynamical systems, signal processing, network analysis, structures and logistics.

The numerical linear algebra part of the unit focuses on matrix decompositions: The information they reveal, the problem they solve, and how they are computed. Particular emphasis will be placed on eigenvalue and singular value decompositions and methods for the (approximate) solution to linear equations. The optimisation part of the unit will focus on convex optimisation problems, with an emphasis on linear and quadratic programming problems. You will learn to recognise engineering problems that can be modelled as convex optimisation problems, apply appropriate numerical methods to solve these problems and explain how structural features of these problems affect the performance of numerical algorithms.