EG551T: MATHEMATICAL OPTIMISATION (2015-2016)

Course Aims

To provide MEng students with a range of advanced engineering analysis techniques in terms of mathematical optimisation and software development, applicable over a range of engineering disciplines.

Main Learning Outcomes

A range of advanced mathematical optimisation techniques used in engineering analysis, applicable over a range of engineering disciplines, is studied. Techniques of mathematical optimisation are used as the basis for much engineering synthesis and the solution of inverse problems. In addition, the student will learn general techniques for the analysis of a given problem and how to break this down into its component parts.  Students carry out practical exercises using MATLAB

By the end of the course students should:
A) have knowledge and understanding of:
• general techniques of mathematical optimisation
• methods of mathematical minimisation
• optimisation problems arising in engineering applications
• optimisation algorithms for 1-dimensional problems
• gradient methods for multi-dimensional optimisation
• optimisation methods for constrained and unconstrained problems
• methods of problem analysis
B) have gained intellectual skills so that they are able to:
• distinguish local and global optimisation schemes and their applicability
• describe how optimisation problems arise in engineering applications
• formulate optimisation algorithms for 1-dimensional problems
• derive and apply gradient methods to multi-dimensional optimisation
• apply optimisation methods to constrained and unconstrained problems
• solve specific engineering problems of some complexity
• approach any given problem and break it down for solving through software
C) have gained practical skills so that they are able to:
• use MATLAB to solve advanced engineering problems
• use flowcharts and pseudo code to solve or describe a given problem
D) have gained or improved transferable skills so that they are able to:
• write technical reports dealing with difficult engineering problems

Course Content

General techniques of mathematical optimisation and minimisation. Methods for one variable: Newton's method; Fibonacci search; Golden-section search; Curve fitting approaches using Quadratic interpolation, Cubic interpolation; Brent's method. Methods for many variables: Direct search methods using Hooke and Jeeves' method, Downhill simplex (Nelder and Mead's) method; Gradient methods using the method of steepest descent, Quadratic functions, Newton-Raphson method, Conjugate directions, Fletcher-Reeves method, Davidson-Fletcher-Powell method. Constrained Optimisation: Equality constrains, Inequality constrains, Convexity and Concavity.

Discipline specific applications. Modelling data using Non-linear least squares, Levenberg-Marquardt algorithm. Local and global optimisation using Simulated annealing, Genetic algorithms; Inverse problems; Regularisation; Applications of Local and global optimisation: simulated annealing and genetic algorithms in engineering problem solving procedures. Other Applications specific to engineering disciplines.

Information on contact teaching time is available from the course guide.

More Information about Week Numbers

1st Attempt

1 three-hour written examination paper (100%), made up of a number of questions that are all compulsory. This examination will cover materials used in the lectures, tutorials and computer tutorials.

Resit

1 three-hour written examination paper (100%), made up of a number of questions that are all compulsory.

a) Students can receive feedback on their progress with the Course on request at the weekly tutorial/computer laboratory sessions.
b) There will be tutorial sessions dedicated solely to feedback on sample exam paper questions at various times through the course.
c) Students requesting feedback on their exam performance should make an appointment during the scheduled feedback session which will be announced within 4 weeks of the publication of the exam results.