Optimisation

Learning Outcomes

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

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

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.

Summative

Summative assessment description

Repeat Information

Repeat type: Internal & External