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).

Academic session

2018-19

Module

Numerical Optimisation

Code

COMP0120

Module delivery

1819/A7P/T2/COMP0120 Postgraduate

Related deliveries

None

Prior deliveries

COMPGV19

Level

Postgraduate

FHEQ Level

L7

FHEQ credits

15

Term/s

Term 2

Module leader

Betcke, Marta

Contributors

Betcke, Marta

Module administrator

Horslen, Caroline

Aims

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.

Learning outcomes

On successful completion of the module, a student will be able to:

  1. practically understand a comprehensive set of optimization techniques and their range of applicability.
  2. implement mathematical methods.
  3. apply these techniques to problems they encounter in their studies e.g. MSc project/dissertation and later in their professional carrier.
  4. 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:

  • MRes Robotics
  • MSc Computational Finance
  • MSc Computational Statistics and Machine Learning
  • MSc Computer Graphics, Vision and Imaging
  • MSc Machine Learning
  • MSc Robotics and Computation

Prerequisites:

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.

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.

Syllabus

  • 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.

Delivery

The module is delivered through a combination of lectures, tutorials, programming exercises and project work.

Assessment

This module delivery is assessed as below:

#

Title

Weight (%)

Notes

1

Project (2,000 words)

40

Can be resat in LSA period

2

Project proposal (2,000 words)

20

Can be resat in LSA period

3

In-class exercises

40

LSA resit: individual essay substitute

In order to pass this module delivery, students must achieve an overall weighted module mark of 50%.