# 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).

Code COMPGV19 MSc Basic Linear Algebra and Analysis. 2 Marta Betcke (75%) [Lectures]Kiko Rullan (25%) [Tutorials] 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. 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.

# 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.

# 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)

# Assessment

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.

# Resources

Reading list available via the UCL Library catalogue.