Description
Aims:
The module aims to provide students with an overview of the optimization landscape and a practical understanding of most popular optimization techniques and an ability to apply these methods to problems they encounter in their studies e.g., MSc project/dissertation and later in their professional career.
Intended learning outcomes:
On successful completion of the module, a student will be able to:
- Practically understand a comprehensive set of optimization techniques and their range of applicability.
- Implement mathematical methods.
- Apply these techniques to problems they encounter in their studies e.g. MSc project/ dissertation and later in their professional career.
- Critically evaluate the results, which the methods produced for a given problem.
Indicative content:
This module teaches a comprehensive range of state-of-the-art numerical optimization techniques. It covers a number of approaches to unconstrained and constrained problems, methods for smooth and non-smooth convex problems as well as basics of non-convex optimisation.
The following are indicative of the topics the module will typically cover:
- Mathematical formulation and types of optimisation problems.
- Unconstrained optimization theory e.g.: local minima, first and second order conditions.
- Unconstrained optimization methods e.g.: line-search, trust region, gradient descent, conjugate gradient, Newton, Quasi-Newton, inexact Newton.
- Least Squares problems.
- Constrained optimization theory e.g.: local and global solutions, first order optimality, second order optimality, constraints qualification, equality and inequality constraints, duality, KKT conditions.
- Constrained optimization methods for equality and inequality constraints e.g.: constraints elimination, feasible and infeasible Newton, primal-dual method, penalty, barrier and augmented Lagrangian methods, interior point methods.
- Non-smooth optimization e.g., subgradient calculus, proximal operator, operator splitting, ADMM, non-smooth penalties e.g., L1 or TV.
Requisites:
To be eligible to select this module as an option or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; (2) have strong competency in Linear Algebra and Analysis; (3) have fluency in matrix calculus; and (4) have working knowledge of Matlab.
The coursework assessment needs to be completed using Matlab and all the solutions are provided in Matlab.
Module deliveries for 2024/25 academic year
Last updated
This module description was last updated on 19th August 2024.
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