Nonlinear Programming

The details
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Postgraduate: Level 7
Thursday 05 October 2023
Friday 15 December 2023
08 February 2024


Requisites for this module



Key module for

DIP G20109 Optimisation and Data Analytics,
MSC G20312 Optimisation and Data Analytics,
MPHDG20048 Operational Research,
PHD G20048 Operational Research

Module description

The module 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.

The module has a significant practical component comprising four one-hour computer labs using MATLAB. These will include one on Golden Section, Search and Quadriatic Fit Search, and one on Gradient search, Newton's method and Quasi-Newton methods.

Module aims

The aims of this module are:

  • to extend the concepts of mathematical modelling in operational decision making to nonlinear functions to cover wider real applications such as portfolio, regressions, volumes etc.

  • to Guide students into suitable (numerical) approaches according to the problem properties and systematically introduce the pros and cons of these methodologies.

Module learning outcomes

By the end of this module, students will be expected to be able to:

  1. Carry out a modelling process to convert problems into mathematical form.

  2. Apply an appropriate algorithm or numerical method for solving a particular problem.

  3. Discuss the relative advantages and limitations of the various algorithms and numerical methods.

  4. Discuss and analyse the important features and advantages of quasi-Newton methods.

  5. Use given implementations of these algorithms in Matlab, and observe and analyse the results.

  6. Understand the derivation and uses of the Karush-Kuhn-Tucker necessary conditions for optimality.

Module information

Indicative syllabus

Formulation of unconstrained and constrained nonlinear optimisation models.
One-dimensional search (Golden Section Search, Three Point Pattern, Quadratic Fit Search).
Conditions for local optimality (Quadratic forms, Taylor series for multiple variables, Gradient Theorem).
Gradient search, Newton's method, Quasi-Newton methods.
Lagrange multiplier methods.
Karush-Kuhn-Tucker optimality conditions.

Learning and teaching methods

Teaching in the School will be delivered using a range of face to face lectures, classes and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.


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 Coursework weighting
Coursework   Assignment 1      
Coursework   Assignment 2      
Exam  Main exam: In-Person, Open Book (Restricted), 120 minutes during Summer (Main Period) 
Exam  Reassessment Main exam: In-Person, Open Book (Restricted), 120 minutes during September (Reassessment Period) 

Exam format definitions

  • Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
  • In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
  • In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
  • In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary, for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.

Your department will provide further guidance before your exams.

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
20% 80%
Module supervisor and teaching staff
Prof Xinan Yang, email:
Professor Xinan Yang, Professor Abdellah Salhi



External examiner

Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Available via Moodle
Of 46 hours, 40 (87%) hours available to students:
6 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s), module, or event type.


Further information

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