COMP0120 Numerical Optimisation
This database contains the 2018-19 versions of syllabuses.
Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).
The aim is to provide the 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 carrier.
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 carrier.
- critically evaluate the results, which the methods produced for a given problem.
Availability and prerequisites
This module delivery is available for selection on the below-listed programmes. The relevant programme structure will specify whether the module is core, optional, or elective.
In order to be eligible to select this module as optional or elective, where available, students must meet all prerequisite conditions to the satisfaction of the module leader. Places for students taking the module as optional or elective are limited and will be allocated according to the department’s module selection policy.
Programmes on which available:
In order to be eligible to select this module, students must have a strong competency in Linear Algebra and Analysis. Fluency in matrix calculus and working knowledge of Matlab is assumed. The coursework (8x5%) needs to be completed using Matlab and all the solutions are provided in Matlab.
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.
- 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.
An indicative reading list is available via http://readinglists.ucl.ac.uk/departments/comps_eng.html.
The module is delivered through a combination of lectures, tutorials, programming exercises and project work.
This module delivery is assessed as below:
Project (2,000 words)
Can be resat in LSA period
Project proposal (2,000 words)
Can be resat in LSA period
LSA resit: individual essay substitute
In order to pass this module delivery, students must achieve an overall weighted module mark of 50%.