Credit points: 15
Optimisation is the process of maximizing or minimizing some objective of interest, while satisfying constraints. Optimisation problems are fundamental and ubiquitous in the study of machine learning, signal processing, and statistics. This subject will develop the mathematical theory, introduce useful tools, and explain the algorithms and their implementation. A variety of distinct optimisation problem types will be encountered including linear, quadratic, and integer programming, as well as various unconstrained problems. Real world instances of such problems will be considered, and solution methods for such problems will be studied. A basic knowledge of calculus and real analysis is assumed.
SchoolSchool Engineering&Mathematical Sciences
Subject Co-ordinatorPeter Van Der Kamp
Available to Study Abroad StudentsNo
Subject year levelYear Level 5 - Masters
Prerequisites Must be admitted in one of the following courses: SHS (in mathematics, statistics), SHCS, SMDS.
Graduate capabilities & intended learning outcomes
01. Translate real-world problems into mathematical form, using the language of optimisation theory.
- Modelling is discussed in the online modules. In practice classes, student will learn how variables, objectives, and constraints are defined in different situations.
02. Synthesise information, concepts and theories of unconstrained optimisation, and of linear, quadratic, and integer programming.
- The concepts and theory of various optimization problems will be introduced in the online modules. Practice class questions are designed to reinforce the concepts and develop understanding of the theories.
03. Employ tools and implement solution methods and algorithms for unconstrained optimisation, and linear, quadratic, and integer programming.
- Tools and algorithms are introduced, and implementations are explained and discussed in online modules. In practice classes students will familiarize themselves with these tools. They will practice solving problems and implementing the algorithms. These implementations will require students to consider the specifics of problem instances.
04. Apply optimisation techniques to a range of practical problems.
- Real world optimisation problems and their solutions will be introduced in online modules. In the practice classes, and for the investigation, students will practice solving optimisation problems.
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Melbourne, 2019, Semester 1, Blended
Maximum enrolment sizeN/A
Subject Instance Co-ordinatorPeter Van Der Kamp
One 2.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
"Classes will be in a computer lab"
One 2.0 hours directed reading per week on any day including weekend during the day from week 10 to week 22 and delivered via online.
"Readings and video clips"
|Sets of mathematical problems (each equiv. to 800 words)||Assignments are sets of problems, where emphasis is placed on implementation of algorithms and use of software tools.||30||01, 02, 03|
|One written investigation (equiv. to 1600 words)||The written investigation is a literature study/review or an in-depth treatment of a real world optimisation problem.||20||02, 03, 04|
|One 2 hour exam (2000 words equivalent)||The exam is a set of problems, where emphasis is placed on modelling, concepts, and theories.||50||01, 02, 04|