Unit information: Optimisation in 2020/21

Unit name	Optimisation
Unit code	MATH30017
Credit points	20
Level of study	H/6
Teaching block(s)	Teaching Block 2 (weeks 13 - 24)
Unit director	Dr. Tadic
Open unit status	Not open
Pre-requisites	MATH10003 Analysis 1A and MATH10006 Analysis 1B (or MATH10011 Analysis), MATH11007 Calculus 1 (or MATH10012 ODEs, Curves and Dynamics), and MATH11005 Linear Algebra and Geometry MATH20901 Multivariable Calculus is desirable but not essential
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit Aims

The aim of this unit is to make students acquainted with the main concepts, ideas, methods, tools and techniques of the mathematical optimisation.

Unit Description

Optimisation can be described as the processes of selecting a best solution (or a decision) out of available alternatives. As such, optimisation is involved in a number of human activities and almost all branches of natural sciences.

For example, investors seek to create portfolios avoiding excessive risk and achieving high return rates. Manufactures aim to maximize the efficiency of their production processes. Engineers adjust parameters to optimise the performance of their designs. Physical systems tend to a state of a minimum energy. Molecules in an isolated system tend to react with each other until the total potential energy is minimized. Rays of light follow paths minimising their travel time.

Mathematically speaking, optimisation is the process of minimising (or maximizing) a multivariable function subject to constraints on its variables.

Intended Learning Outcomes

At the end of the unit, the students should:

• understand the basic theoretical aspects of optimisation problems.
• understand the numerical methods for optimisation problems and their properties.
• be able to solve simple optimisation problems by hand.
• be able to solve (relatively) simple optimisation problems numerically.

Teaching Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

80% Timed, open-book examination 20% Coursework: computing assignments

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• M.S. Bazaraa, John J. Jarvis and Hanif D. Sherali, Linear Programming and Network Flows, Wiley 2009
• M.S. Bazaraa, Hanif D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, Wiley 2006
• Dimitris Bertsekas, Nonlinear Programming, Athena Scientific, 2016
• Dimitris Bertsimas and John N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific 1997
• J. Frédéric Bonnans, J. Charles Gilbert, Claude Lamerechal and Claudia A. Sagastizabal, Numerical Optimization: Theory and Practical Aspects, Springer 2006
• Jorge Nocedal and Stephen J. Wright, Numerical Optimization, Springer 2006