MATH412-12S2 (C) Semester Two 2012

Unconstrained Optimization

0.1250 EFTS
09 Jul 2012 - 11 Nov 2012


Unconstrained Optimization

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:

Critically competent in a core academic discipline of their award

Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.


Subject to approval of the Head of Department.

Streams Day Time Where Notes
Stream 01 Tuesday 4:00pm-5:00pm Erskine 441 9 Jul - 19 Aug,
3 Sep - 14 Oct
Wednesday 9:00am-10:00am Erskine 441 9 Jul - 19 Aug,
3 Sep - 14 Oct

Course Coordinator / Lecturer

Chris Price (MATH)


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

Examination and Formal Tests

Exam Thursday 08 Nov 2012 2:30pm-4:30pm  


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 $788.00

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

For further information see Mathematics and Statistics.

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