COMPGV19 - Numerical Optimisation
This database contains the 2017-18 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).
|Prerequisites||Basic Linear Algebra and Analysis.|
Marta Betcke (75%) [Lectures]
Kiko Rullan (25%) [Tutorials]
|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.|
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.