MTH4330 Optimisation and operations research
Faculty of Science
MTH4330 Optimisation and operations research is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2025 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2025
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
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Requisites
Before MTH4330
No prerequisites or corequisites besides the enrolment rules below.
After MTH4330
No unit lists MTH4330 as a prerequisite in the 2025 handbook.
Enrolment rules
You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics
Prohibition: MTH3330
Overview
This unit introduces some of the fundamental concepts and algorithms of mathematical optimisation. Optimisation underpins many parts of both data analytics (machine learning) and business analytics (management science/operations research). The concepts and approaches taught in this unit will be illustrated using examples from both types of analytics, such as training ML models and planning models arising in supply chain optimisation. The unit provides an introduction to the mathematics of continuous optimisation with focus on iterative gradient descent methods, linear programming and network optimisation. It covers both the underpinning theory, such as convergence analysis and duality, and the practical implementation of optimisation algorithms
Offerings in 2025
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Demonstrate an in-depth understanding of necessary and sufficient optimality conditions for optimisation problems
- 2
Analyse and synthesise the mathematical principles behind advanced iterative algorithms for solving unconstrained nonlinear optimisation problems, demonstrating a deep understanding of their theoretical foundations.
- 3
Formulate as an optimisation problem the task of training a machine learning model and select and justify an appropriate optimisation algorithm
- 4
Demonstrate an understanding of Lagrangian duality and the use of non-smooth optimisation methods to solve Lagrangian dual problems.
- 5
Formulate a range of operations research problems as linear programming problems, and solve them using computational techniques
- 6
Exhibit a comprehensive understanding of how the most widely used linear programming algorithms operate.
- 7
Apply duality theory to prove the optimality of solutions for linear programming problems, demonstrating expertise in theoretical and practical aspects.
- 8
Solve complex network optimisation problems using specialised algorithms, showcasing advanced problem-solving skills and the ability to handle intricate optimisation challenges
Workload and teaching
- Workshops36 hours
- Applied sessions22 hours
- Teaching approachActive learning
Two 1.5-hour workshops;
One 2-hour applied class (in weeks 2-12) and
7 hours of independent study per week.
Learning resources
Required resources
Most of the content of this unit is covered in the following two textbooks:
1. Luenberger & Ye, “Linear and nonlinear programming” 2016 (4th edition).
2. Nodeal & Wright "Numerical Optimization" 2006 (2nd edition)
Both of these are available electronically from the library.
Technology_resources: Computer for completing computational exercises
Contacts
- Chief Examiners
- Professor Andreas Ernst
- Unit Coordinators
- Professor Andreas Ernst
Common questions
What are the prerequisites for MTH4330?
MTH4330 has no prerequisites, but enrolment rules apply.
When is MTH4330 offered?
In 2025, MTH4330 runs in Semester 1 at Clayton.
Does MTH4330 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.