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 … For more content click the Read More button below. 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.

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.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Requisites

Prerequisite

Contacts

Chief Examiner(s)

Dr James Saunderson

Unit Coordinator(s)

Dr James Saunderson

Learning outcomes

On successful completion of this unit, you should be able to:

Formulate appropriate engineering problems using linear systems of equations and convex optimisation problems.

Analyse the properties of linear systems of equations and optimisation problems that affect the performance of numerical algorithms to solve those problems.

Apply suitable numerical methods to solve linear systems of equations and convex optimisation problems.

Use matrix decompositions to simplify, approximate and analyse linear systems of equations and optimisation problems.

Teaching approach

Problem-based learning

Online learning

Active learning

Assessment summary

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

1 - Assignments

2 - Quizzes

3 - Workshop-related activities

4 - Final assessment

Scheduled and non-scheduled teaching activities

Practical activities

Workshops

Workload requirements

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.

Learning resources

Required resources

Availability in areas of study

Minor: Computational engineering