ECE3093 · Optimisation and numerical methods for engineers

Overview

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.

Areas of study: Minor: Computational engineering Minor: Networks for connectivity Minor: Smart manufacturing Minor: Artificial intelligence in engineering

Offerings

Assessment

The Handbook lists an examination for this unit.

Continuous assessment: 40% Final assessment: 60% This unit contains threshold hurdle requirements that you must achieve to be able to pass the unit. You are required to achieve at least 45% in the total continuous assessment component and at least 45% in the final assessment component. The consequence of not achieving a hurdle requirement is a fail grade (NH) and a maximum mark of 45 for the unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Formulate appropriate engineering problems using linear systems of equations and convex optimisation problems.
2. Analyse the properties of linear systems of equations and optimisation problems that affect the performance of numerical algorithms to solve those problems.
3. Apply suitable numerical methods to solve linear systems of equations and convex optimisation problems.
4. Use matrix decompositions to simplify, approximate and analyse linear systems of equations and optimisation problems.

Workload

The minimum total expected workload to achieve the learning outcomes for this unit is 144 hours per semester typically comprising a mixture of 3-6 hours of scheduled learning activities and 6-9 hours of independent study per week. Scheduled activities may include a combination of teacher-directed learning, peer-directed learning and online engagement. Independent study may include associated readings, assessment and preparation for scheduled activities.

Student experience, not official rules. Nothing here changes what the Handbook says.