Course Title: Optimisation

Part A: Course Overview

Course Title: Optimisation

Credit Points: 12.00

Terms

Course Code

Campus

Career

School

Learning Mode

Teaching Period(s)

MATH2390

City Campus

Undergraduate

171H School of Science

Face-to-Face

 Sem 2 2021,
Sem 2 2022,
Sem 2 2023

Course Coordinator: Andrew Eberhard

Course Coordinator Phone: +61 3 9925 2616

Course Coordinator Email: andy.eberhard@rmit.edu.au

Course Coordinator Location: 15.04.004

Course Coordinator Availability: By appointment, by email


Pre-requisite Courses and Assumed Knowledge and Capabilities

Required Prior Study

You should have satisfactorily completed following course/s before you commence this course.

Alternatively, you may be able to demonstrate the required skills and knowledge before you start this course.

Contact your course coordinator if you think you may be eligible for recognition of prior learning.

Assumed Knowledge

You are assumed to have completed an introductory course in vector calculus, and have some familiarity with computing and the writing of simple programs in the MATLAB programming language:


Course Description

Optimisation problems arise in many areas of engineering, science, economic modelling, resource modelling and operations research. These problems can arise via the need to find a best approximation or ‘fit’ to a set of data or to use finite resources equitably and efficiently. Indeed, many physical laws are governed by the principle of least action. The solution of such problems often requires the use of modern digital computers and algorithms to approximate a solution. This course gives an introduction to the main ideas behind these algorithms and the mathematical theory underpinning their use. We consider what leads to convergence and efficiency for various algorithms. MATLAB, a modern computer programming language will be used to implement some algorithms to illustrate these principles. Skills in formulation and the reformulation of optimization problems will be introduced both in problem classes and using specific examples. Certain problem classes have associated with them an efficient solver and we will practise calling standard solvers for these problems and interpreting the output. Examples of problems will be sort from statistics, machine learning and mathematical modelling.


Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 Bachelor of Science (Applied Mathematics and Statistics) and BP331 Bachelor of Analytics):   PLO2. Knowledge and Technical Competence: • use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.   PLO3. Problem-solving: • synthesise and flexibly apply knowledge to characterise, analyse and solve a wide range of problems • balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.


Upon successful completion of this course, you should be able to :

  1. Model a real-word problem as an optimisation program and discuss the limits of the model and how its solutions can contribute to decision-making.
  2. Contrast the relationship between different formulations of the same problem and how these solutions relate to each other.
  3. Explain how the mathematical basis for optimisation methods can be related poor behaviour of an algorithm when applied to a particular problem, and recommend an ameliorated strategy.
  4. Differentiate between various optimisation problem classes and explain which optimisation solver is suitable for each class of problem. Call on some of these solvers to solve problems and interpreting the output.
  5. Analyse the mathematical properties of an optimisation problem and select the most appropriate methods to solve it.


Overview of Learning Activities

You will be actively engaged in a range of learning activities such as lectorials, tutorials, practicals, laboratories, seminars, project work, class discussion, individual and group activities. Delivery may be face to face, online or a mix of both.

You are encouraged to be proactive and self-directed in your learning, asking questions of your lecturer and/or peers and seeking out information as required, especially from the numerous sources available through the RMIT library, and through links and material specific to this course that is available through myRMIT Studies Course.


Overview of Learning Resources

RMIT will provide you with resources and tools for learning in this course through myRMIT Studies Course.

There are services available to support your learning through the University Library. The Library provides guides on academic referencing and subject specialist help as well as a range of study support services. For further information, please visit the Library page on the RMIT University website and the myRMIT student portal.

A Library Guide is available at: http://rmit.libguides.com/mathstats


Overview of Assessment

Assessment Tasks

Assessment Task 1: Two take home written assignments
Weighting 2 x 15% = 30%
This assessment task supports CLOs 1, 2, 3, 4 & 5

Assessment Task 2: Practical computer laboratory session
Weighting 40%
This assessment task supports CLOs 3, 4 & 5

Assessment Task 3: Weekly in class quiz
Weighting 10%
This assessment task supports CLOs 1, 2, 3, 4 & 5

Assessment Task 4: End of semester online, timed, summative quiz
Weighting 20%
This assessment task supports CLOs 1, 2, 3, 4 & 5

If you have a long-term medical condition and/or disability it may be possible to negotiate to vary aspects of the learning or assessment methods. You can contact the program coordinator or Equitable Learning Services if you would like to find out more.