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.
Prerequisites: MATH1054 OR MATH1055 OR MATH1010 OR MATH1015
Aims and Objectives
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Understanding the basic optimization theory including optimality conditions and duality theory
- Demonstrate knowledge and understanding of the basic ideas underlying optimization techniques
- 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
Subject Specific Intellectual and Research Skills
Having successfully completed this module you will be able to:
- Develop mathematical optimization models for a range of practical problems
- Appreciate the power of using the mathematical approach to optimization problems relevant to engineering
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
|Total study time||150|
Resources & Reading list
Vanderbei, R. (2014). Linear programming: Foundation and Extension. Springer.
Stephen Boyd, Lieven Vandenberghe (2004). Convex optimization. Imprint:Cambridge: Cambridge University Press.
Nocedal, J and Wright, S (2006). Numerical Optimization. New York: Springer.
Frederick S. Hillier, Gerald J. Lieberman (2010). Introduction to operations research. McGraw-Hill.
Summative assessment description
Repeat type: Internal & External