MTH4330 · Optimisation and operations research

Overview

This unit introduces some of the fundamental concepts and algorithms of mathematical optimisation. Optimisation underpins many parts of both data analytics (machine learning) and business analytics (management science/operations research). The concepts and approaches taught in this unit will be illustrated using examples from both types of analytics, such as training ML models and planning models arising in supply chain optimisation. The unit provides an introduction to the mathematics of continuous optimisation with focus on iterative gradient descent methods, linear programming and network optimisation. It covers both the underpinning theory, such as convergence analysis and duality, and the practical implementation of optimisation algorithms

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Explain and apply the mathematical theory of optimisation, including optimality conditions, iterative algorithms for nonlinear problems, and the principles of duality and non-smooth optimisation;
2. Formulate and analyse optimisation problems arising in machine learning, operations research, and network optimisation, selecting and justifying appropriate algorithms;
3. Implement and evaluate linear programming and related optimisation algorithms, proving optimality where appropriate and applying them to real-world data and applications;
4. Communicate optimisation reasoning and results effectively, both orally and in writing, and collaborate in small groups to solve problems;
5. Extend and deepen understanding of time series methods through advanced model synthesis, rigorous analysis, and independent application to complex or novel datasets.

Workload

Two 1.5-hour workshops; One 2-hour applied class (in weeks 2-12) and 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.