MA427      Half Unit
Mathematical Optimisation

This information is for the 2020/21 session.

Teacher responsible

Dr Giacomo Zambelli


This course is available on the Global MSc in Management, Global MSc in Management (CEMS MiM), Global MSc in Management (MBA Exchange), MSc in Applicable Mathematics, MSc in Operations Research & Analytics, MSc in Statistics, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (LSE and Fudan), MSc in Statistics (Financial Statistics) (Research), MSc in Statistics (Research), MSc in Statistics (Social Statistics) and MSc in Statistics (Social Statistics) (Research). This course is available as an outside option to students on other programmes where regulations permit.


Students must have sufficient knowledge of linear algebra (linear independence, determinants, matrix inversion and manipulation) and of basic multivariate calculus (derivatives and gradients).

Course content

Introduction to the theory and solution methods of linear and nonlinear programming problems, including: linear programming duality, Lagrangian duality, convex programming and Karush-Kuhn-Tucker conditions, algorithms for linear and convex optimisation problems, theory of good formulations for integer linear programming models, integer linear programming methods (branch and bound and cutting planes).


This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos. 

Formative coursework

Weekly exercises will be given that will be solved and discussed during the seminars. Three of those exercises will be handed in as formative coursework and the students will be given feedback on their submissions.

Indicative reading

Extensive lecture notes covering all parts of the course will be provided. Students interested in further readings can look at the books below.

  • D Bertsimas and J N Tsitsiklis, Introduction to Linear Optimization (1997)
  • S Boyd and L Vandenberghe, Convex Optimization (2004)
  • M Conforti, G Cornuejols, G Zambelli, Integer Programming (2014)


Exam (100%, duration: 3 hours) in the summer exam period.

The exam will take place online.

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: 30

Average class size 2019/20: 15

Controlled access 2019/20: Yes

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Problem solving
  • Application of numeracy skills
  • Specialist skills