MA427      Half Unit
Nonlinear Optimisation and Applications

This information is for the 2025/26 session.

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Requisites

Additional requisites:

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

This course is an introduction to the theory and implementation of nonlinear optimisation. Students will develop both theoretical understanding and practical skills in solving complex optimisation problems.

The course will begin with some of the fundamental theory of convex and nonconvex optimisation, including Lagrangian duality and the Karush-Kuhn-Tucker optimality conditions. Various algorithms for solving constrained and unconstrained nonlinear optimisation problems will be discussed in detail, both in terms of theoretical efficiency guarantees and practical implementation considerations. First-order methods such as gradient descent and its variants will be the primary focus.

A key component of the course is the application of optimisation methods, with a particular focus on applications to machine learning.

15 hours of seminars and 20 hours of lectures in the Winter Term.

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.

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

• S Boyd and L Vandenberghe, Convex Optimization (2004)
• N Vishnoi, Algorithms for Convex Optimization (2021)

Exam (100%), duration: 180 Minutes in the Spring exam period