Nonlinear Programming

The details
Mathematical Sciences
Colchester Campus
Postgraduate: Level 7
Thursday 03 October 2019
Saturday 14 December 2019
01 October 2019


Requisites for this module



Key module for

DIP G10109 Mathematics,
MSC G10112 Mathematics,
MSC G10124 Mathematics,
DIP G20109 Statistics and Operational Research,
MSC G20312 Statistics and Operational Research

Module description

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.

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.

Module aims


Nonlinear programming
- 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.

Module learning outcomes

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.

Module information

No additional information available.

Learning and teaching methods

There are 21 lectures, 10 classes and 4 labs in total. There will be regular assessed material at postgraduate level which will be discussed in one of the classes. In the Summer term 3 revision lectures are given.


This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework Lab Report 1 04/11/2019 50%
Coursework Lab Report 2 09/12/2019 50%
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Dr Xinan Yang, email
Dr Xinan Yang (



External examiner

Prof Fionn Murtagh
Professor of Data Science
Available via Moodle
Of 38 hours, 34 (89.5%) hours available to students:
4 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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