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UNCONSTRAINED OPTIMISATION

Module code: EE403FZ
Credits: 5
Semester: 2
Department: INTERNATIONAL ENGINEERING COLLEGE
International:

	Overview
	� To introduce the field of unconstrained optimisation. � To outline basic line search methods for 1-variable functions � To outline basic direct and gradient-based search methods for multi-variable functions. � Fundamental principles of optimization � Line searches for functions with one variable - Grid, Fibonacci, Golden Section & Quadratic � Direct search methods for functions of more than one variable - Univariate, DSC algorithm, Gram-Schmidt Orthogonalisation & Simplex method � Gradient methods for functions of more than one variable - Steepest Descent, Conjugate Gradient Algorithm � Fletcher & Reeves � Hessian-based Gradient methods for functions of more than one variable - Newton�s method, Quasi-Newton�s method, DFP & BFGS algorithms � The Sum of Squares Problem - Gauss-Newton and Levenberg-Marquart algorithms � An introduction to constrained optimisation

Overview

� To introduce the field of unconstrained optimisation.
� To outline basic line search methods for 1-variable functions
� To outline basic direct and gradient-based search methods for multi-variable functions.

� Fundamental principles of optimization
� Line searches for functions with one variable
- Grid, Fibonacci, Golden Section & Quadratic
� Direct search methods for functions of more than one variable
- Univariate, DSC algorithm, Gram-Schmidt Orthogonalisation & Simplex method
� Gradient methods for functions of more than one variable
- Steepest Descent, Conjugate Gradient Algorithm � Fletcher & Reeves
� Hessian-based Gradient methods for functions of more than one variable
- Newton�s method, Quasi-Newton�s method, DFP & BFGS algorithms
� The Sum of Squares Problem
- Gauss-Newton and Levenberg-Marquart algorithms
� An introduction to constrained optimisation

	Learning Outcomes
	On successful completion of the module, students should be able to: Carry out basic line searches for functions with one variable. Apply direct search methods to functions of more than one variable. Apply gradient-based methods to functions of more than one variable. Apply hessian-based methods to functions of more than one variable. Solve the �sum of squares� problems using the Gauss-Newton method.

Learning Outcomes

Teaching & Learning methods

Assessment

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes 1 x 2 hour written examination (Autumn). The continuous assessment mark is carried forward as there is no facility for repeating the continuous assessment elements of the course. University scheduled written examination (Autumn): 120 minutes, On-campus

	Additional Reading
	Reference Reading: Singiresu S. Rao, Engineering Optimization, Theory and Practice Brian D. Bunday, Basic Opimisation Methods E. M. L. Beale, Introduction to Opimization R. Fletcher, Practical Methods of Optimisation Rangarajan K. Sundaram , A First Course in Optimization Theory J. J. McKeown, D. Meegan, D. Sprevak, An Introduction to Unconstrained Optimisation

	Timetable
	This timetable is not currently available, please contact the International Engineering College Department.

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Courses / Module

UNCONSTRAINED OPTIMISATION