COMPGV19 - Numerical Optimisation

This database contains the 2017-18 versions of syllabuses. Syllabuses from the 2016-17 session are available here.

Note: Whilst every effort is made to keep the syllabus and assessment records correct, the precise details must be checked with the lecturer(s).

PrerequisitesBasic Linear Algebra and Analysis.
Taught By

Marta Betcke (75%) [Lectures]

Kiko Rullan (25%) [Tutorials]

AimsThe 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
  • Practical understanding of a comprehensive set of optimization techniques and their range of applicability.
  • Ability to implement mathematical methods.
  • Ability to apply these techniques to problems they encounter in their studies e.g. MSc project/dissertation and later in their professional carrier.
  • Ability to critically evaluate the results, which the methods produced for a given problem.


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.

Method of Instruction

Lectures totaling 30 hours (2 x 2 hours weekly over 7.5 out of 10 weeks) and tutorials totaling 10 hours (1 x 1 hour weekly over 10 weeks)


The course has the following assessment components:

  • Coursework 1 (20%)
    • Unconstraint optimisation (4 short assignments, 5% each)
  • Coursework 2 (20%)
    • Constraint optimisation (4 short assignments, 5% each)
  • Project (60%)
    • Project Proposal (2000 words, 20%)
    • Project (300 words + code, 40%)

To pass this course, students must:

  • Obtain an overall pass mark of 50% for all sections combined.


Reading list available via the UCL Library catalogue.