Optimisation | MATH3082 | University of Southampton

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

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

Demonstrate knowledge and understanding of the basic ideas underlying optimization techniques
Understanding the basic optimization theory including optimality conditions and duality theory
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:

Appreciate the power of using the mathematical approach to optimization problems relevant to engineering
Develop mathematical optimization models for a range of practical problems

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

Study time
Type	Hours
Independent Study	94
Teaching	56
Total study time	150

Resources & Reading list

Textbooks

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.

Assessment

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Exam	85%
Coursework assignment(s)	15%

Repeat Information

Repeat type: Internal & External