MA305-7-AU: NONLINEAR PROGRAMMING
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: No Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
|Module is taught during the following terms
The module provides an understanding at postgraduate level of nonlinear programming. It contains an introduction to the theory, algorithms and applications of nonlinear programming. It teaches principles of good modelling, from formulation of practical problems to computer solution, and how to design a range of algorithms and numerical methods. It acquaints students with general issues concerning computational algorithms, and considers application areas such as mathematical finance.
- Formulation of unconstrained and constrained nonlinear optimisation models.
- One-dimensional search (Newton-Raphson, golden section search)
- Conditions for local optimality (quadratic forms, convex and concave functions, Taylor series for multiple variables).
- Gradient search, Newton's method, Quasi-Newton methods.
- Lagrange multiplier methods.
- Karush-Kuhn-Tucker optimality conditions.
- Penalty function methods.
- Non-derivative methods.
The module has a significant practical component comprising four one-hour computer labs using the Matlab computer package. These will include practicals on Newton-Raphson and golden section search, and on Gradient search, Newton's method and Quasi-Newton methods.
On completing the module, students should be able to:
- carry out a modelling process to convert problems into mathematical form
- apply an appropriate algorithm or numerical method for solving a particular problem;
- discuss the relative advantages and limitations of the various algorithms and numerical methods;
- discuss and analyse the important features and advantages of quasi-Newton methods
- use given implementations of these algorithms in Matlab, and observe and analyse the results;
- understand the derivation and uses of the Karush-Kuhn-Tucker necessary conditions for optimality.
Learning and Teaching Methods
There are 5 lectures and two classes in every fortnight. There will be regular assessed material at postgraduate level which will be discussed in one of the fortnightly classes. In addition there are 4 1-hour computer classes. In the Summer term 3 revision lectures are given.
20 per cent Coursework Mark, 80 per cent Exam Mark
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information
Exam Duration and Period
2:00 hour exam during Summer Examination period.
- Recommended reading:
W. L. Winsten, (2004) Operational Research: Applications and Algorithms, fourth edition. Duxbury Press.
R.L. Rardin. (1998). Optimization in Operations Research, Prentice Hall.