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 … For more content click the Read More button below.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Andreas Ernst

Unit Coordinator(s)

Professor Andreas Ernst

Notes

You are required to bring your own device, such as a laptop, on which you can complete computational exercises, to the applied classes.

This Level 4 unit and its Level 3 counterpart MTH3330 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

On successful completion of 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

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Workshops

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.

Miscellaneous items required (Unit course reader, Printing, Stationery) - $120

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics