MA305-7-AU-CO:
Nonlinear Programming
2024/25
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Autumn
Postgraduate: Level 7
Current
Thursday 03 October 2024
Friday 13 December 2024
15
21 May 2024
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 introduction to the theory and applications of nonlinear programming. It teaches formulation of practical problems 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 two on Golden Section Search, Three Point Pattern and Quadratic Fit Search, and two on Gradient search, Newton's method and Quasi-Newton methods.
The aims of this module are:
- To systematically understand mathematical modelling involving nonlinear functions, with a focus on how nonlinear optimisation contribute to the current real applications/advances in portfolio, regression and machine learning.
- To critically evaluate analytical and numerical methodologies for nonlinear optimisation, discover their pros and cons through guided experiments.
By the end of the module, students will be expected to be able to:
- Carry out self-directed analysis to choose appropriate approaches or numerical methods for solving a particular problem.
- Demonstrate systematic understanding of the learnt approaches and the relative advantages and limitations.
- Independently implement suitable algorithms or packages in Matlab for nonlinear optimisation, clearly communicate their results/conclusions in writing.
- Systematically understand the derivation and uses of the Karush-Kuhn-Tucker necessary conditions for optimality.
Indicative syllabus
- Formulation of unconstrained and constrained nonlinear optimisation models
- One-dimensional search (Golden Section Search, Three Point Pattern and Quadratic Fit Search)
- Conditions for local optimality (Quadratic forms and definiteness, Taylor series for multiple variables, Gradient Theorem)
- Gradient search, Newton's method, Quasi-Newton methods
- Lagrange multiplier methods
- Karush-Kuhn-Tucker optimality conditions
- Convexity
- Penalty method
- Non-derivative method
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 |
|
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| 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
Reassessment
Module supervisor and teaching staff
Prof Xinan Yang, email: xyangk@essex.ac.uk.
Professor Xinan Yang, Professor Abdellah Salhi
maths@essex.ac.uk
Yes
No
No
Dr Yinghui Wei
University of Plymouth
Dr Murray Pollock
Newcastle University
Director of Statistics / Senior Lecturer
Available via Moodle
Of 41 hours, 35 (85.4%) 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.
* Please note: due to differing publication schedules, items marked with an asterisk (*) base their information upon the previous academic year.
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