MTH5331 Nonlinear optimisation
Faculty of Science
MTH5331 Nonlinear optimisation is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2027 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Overview
This unit introduces the theory of nonlinear optimisation, along with numerical methods for solving both unconstrained and constrained problems, and the mathematical foundations that explain their behaviour and convergence.
Topics include convexity, necessary and sufficient optimality conditions, gradient descent, Newton’s method and its variants (globalised, inexact, and quasi-Newton), trust-region methods, projected gradient descent, Newton–Lagrange iteration, penalty methods, and sequential quadratic programming (SQP).
A small practical component focuses on applying nonlinear optimisation techniques to problem-solving, with an emphasis on understanding and formulation rather than implementation
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Demonstrate an advanced understanding of nonlinear optimisation theory at a conceptual level as well as at a granular level;
- 2
Demonstrate an advanced understanding of the uses of common numerical methods for solving unconstrained and constrained optimisation problems, as well as their advantages and disadvantages;
- 3
Apply mathematical principles and theorems to quantify how fast and in what sense these numerical methods converge;
- 4
Select and apply numerical methods for nonlinear optimisation problems in a real-world context;
- 5
Communicate concepts and arguments related to nonlinear optimisation.
Workload and teaching
- Seminars36 hours
- Applied sessions12 hours
- Teaching approachActive learning
- One 2-hour applied class (in weeks 2, 4, 6, 8, 10, 12);
- Two 1.5 -hour seminars and
- Eight hours of independent study per week.
Active learning will occur in seminars and applied sessions.
Contacts
- Unit Coordinators
- Dr Janosch Rieger
- Chief Examiners
- Dr Janosch Rieger
Common questions
What are the prerequisites for MTH5331?
MTH5331 has no prerequisites, but enrolment rules apply.
When is MTH5331 offered?
In 2027, MTH5331 runs in Semester 2 at Clayton.
Does MTH5331 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.