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MA427 Half Unit

Mathematical Optimisation

**This information is for the 2024/25 session.**

**Teacher responsible**

Dr Giacomo Zambelli

**Availability**

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) (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.

**Pre-requisites**

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).

**Teaching**

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Winter Term.

**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)

**Assessment**

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

** Key facts **

Department: Mathematics

Total students 2023/24: 15

Average class size 2023/24: 16

Controlled access 2023/24: Yes

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

- Problem solving
- Application of numeracy skills
- Specialist skills