MA305-7-SP-CO:
Nonlinear Programming
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Sunday 17 January 2021
Friday 26 March 2021
15
15 July 2020
Requisites for this module
(none)
(none)
(none)
(none)
(none)
DIP G20109 Optimisation and Data Analytics,
MSC G20312 Optimisation and Data Analytics,
MPHDG20048 Operational Research,
PHD G20048 Operational Research
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.
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.
Extend the concepts of mathematical modelling in operational decision making to nonlinear functions to cover wider real applications such as portfolio, regressions, volumes etc. Guide students into suitable (numerical) approaches according to the problem properties and systematically introduce the pros and cons of these methodologies.
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.
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, Convex and Concave functions, Taylor series for multiple variables, Gradient Theorem).
- Gradient search, Newton's method, Quasi-Newton methods.
- Lagrange multiplier methods.
- Karush-Kuhn-Tucker optimality conditions.
- Penalty function methods.
- Non-derivative methods.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
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 |
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| Coursework |
Assignment 2 |
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| Exam |
Main exam: 180 minutes during Summer (Main Period)
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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
Reassessment
Module supervisor and teaching staff
Prof Xinan Yang, email: xyangk@essex.ac.uk.
Dr Xinan Yang & Professor Abdel Salhi
Dr Xinan Yang (xyangk@essex.ac.uk), Professor Abdel Salhi (as@essex.ac.uk)
Yes
No
No
Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Available via Moodle
Of 2355 hours, 0 (0%) hours available to students:
2355 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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