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Unit information: Optimisation in 2019/20

Please note: Due to alternative arrangements for teaching and assessment in place from 18 March 2020 to mitigate against the restrictions in place due to COVID-19, information shown for 2019/20 may not always be accurate.

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

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

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



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

Lectures, problem sheets and office hours.

Assessment Information

Formative assessment:

  • weekly problem sheets

Summative assessment:

  • One 2.5h exams (80%)
  • Two computationally oriented homeworks (each 10%)

Reading and References


  • 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