Module overview
The module provides an introduction to the theory and practice of optimization techniques. It covers linear programming as well as nonlinear programming. This module is suitable to those who want to apply computational optimization methods to their problems, which can arise from a variety of applied disciplines such as compuer science and engineering.
Linked modules
Prerequisites: MATH1054 OR MATH1055 OR MATH1010 OR MATH1015
Aims and Objectives
Learning Outcomes
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Appreciate the power of using the mathematical approach to optimization problems relevant to engineering
- Develop mathematical optimization models for a range of practical problems
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Demonstrate knowledge and understanding of some of the most common standard optimization models and how they can be solved, including Simplex methods, gradient methods and Lagrangian function theory
- Understanding the basic optimization theory including optimality conditions and duality theory
- Demonstrate knowledge and understanding of the basic ideas underlying optimization techniques
Syllabus
1. Introduction to optimization modes including linear and nonlinear models
2. Graphical method for linear programming with two variables
3. Simplex methods (Phase I and Phase II methods, Dual simplex method) for linear programming
4. Duality theory and sensitivity analysis
5. Theorems of complementarity and the alternatives
6. Search methods (gradient methods) for nonlinear optimization
7. Lagrangian function theory
8. Practical use of software in solving linear programming
Learning and Teaching
Teaching and learning methods
The module will be taught using lectures and computer labs. The latter is for practically experiencing using software to solve linear programming problems
| Type | Hours |
|---|---|
| Teaching | 56 |
| Independent Study | 94 |
| Total study time | 150 |
Resources & Reading list
Textbooks
Stephen Boyd, Lieven Vandenberghe (2004). Convex optimization. Imprint:Cambridge: Cambridge University Press.
Frederick S. Hillier, Gerald J. Lieberman (2010). Introduction to operations research. McGraw-Hill.
Vanderbei, R. (2014). Linear programming: Foundation and Extension. Springer.
Nocedal, J and Wright, S (2006). Numerical Optimization. New York: Springer.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Coursework assignment(s) | 15% |
| Exam | 85% |
Repeat Information
Repeat type: Internal & External