The University of Southampton
Courses

# MATH3082 Optimisation

## 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.

### Aims and Objectives

#### Module Aims

To be able to solve small sized problems by hand using Simplex Methods and Gradient Methods

#### 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
• 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
##### 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

### 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

TypeHours
Teaching56
Independent Study94
Total study time150

Frederick S. Hillier, Gerald J. Lieberman (2010). Introduction to operations research.

Nocedal, J and Wright, S (2006). Numerical Optimization.

Stephen Boyd, Lieven Vandenberghe (2004). Convex optimization.

Vanderbei, R. (2014). Linear programming: Foundation and Extension.

### Assessment

#### Summative

MethodPercentage contribution
Coursework assignment(s)  () 15%
Exam  (2 hours) 85%

#### Repeat Information

Repeat type: Internal

Prerequisites: MATH1054 or MATH1055 or MATH1010 or MATH1015

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.