EMTH604-12S2 (C) Semester Two 2012

Unconstrained Optimisation

0.1000 EFTS
09 Jul 2012 - 11 Nov 2012


Practical and theoretical aspects of the design and development of algorithms for the optimisation of functions of several variables.

This course looks at the minimization of smooth functions of several variables.  The first part of the course examines gradient based methods using line searches, including Newton, quasi-Newton, and conjugate gradient methods.  

A selection of other topics is then introduced, including trust region methods and methods for constrained optimization.  

Demonstration software is used to illustrate aspects of various algorithms in practice.

• Gradient based methods: steepest descent, conjugate gradients, Newton's method and quasi-Newton methods. Line searches and trust regions.
• Constrained optimization: Karush-Kuhn-Tucker conditions, quadratic penalty functions, augmented Lagrangians.
• Derivative free methods: positive bases, Clarke's generalized derivative, frames.

Learning Outcomes

University Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attributes specified below:


Subject to approval of the Head of Department.

Course Coordinator / Lecturer

Chris Price (MATH)


Assessment Due Date Percentage 
Internal Assessment - TBA 30%
Final Examination 70%


Recommended Texts:

• Numerical Optimization, Nocedal and Wright (2006).
• Practical Methods of Optimisation, Fletcher (1987).
• Practical Optimization, Gill, Murray, and Wright (1981).

Indicative Fees

Domestic fee $703.00

* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.

Minimum enrolments

This course will not be offered if fewer than 5 people apply to enrol.

For further information see Mathematics and Statistics.

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