MA305-6-AU: Nonlinear Programming
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to Study Abroad / Exchange Students: Yes Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No Pre-requisites: MA205 AND MA206
|Module is taught during the following terms
The course provides an introduction to the theory 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.
On completing the course, students should be able to:
- 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;
- 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.
The course has a significant practical component comprising four one-hour computer labs using the MATLAB computer package. These will include one on Newton-Raphson and golden section search,and one on Gradient search, Newton's method and Quasi-Newton methods.
Learning and Teaching Methods
This course runs at 3 hours per week. There are 5 lectures and one class in every fortnight. There will also be four 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.
Available to Socrates/IP students spending all relevant terms at Essex.
- 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.