Optimisation

Module aims

The aim of this module is to equip you with the tools to formulate and solve general constrained and unconstrained optimisation problems. The module covers several introductory topics in optimisation such as necessary and sufficient conditions of optimality, basic optimization algorithms (gradient, Newton, conjugate directions, quasi-Newton), Kuhn-Tucker conditions, penalty method, recursive quadratic programming, and global optimization. Each topic is covered in a mathematical rigorous way with attention to regularity, convergence conditions, and complexity. The module assumes prior basic calculus and linear algebra knowledge such as multivariable calculus, sequences, compactness, and eigenvalues.

Learning outcomes

Upon successful completion of this module, you will be able to:

• Formulate simple unconstrained and constrained optimization problems
• Classify optimal solutions
• Apply the correct methods to solve such problems
• Write basic unconstrained optimization algorithms and assess their convergence and numerical properties
• Apply the notion of penalty in the solution of constrained optimization problems
• Change constrained optimization problems into equivalent unconstrained problems
• Apply basic algorithms for the solutions of global optimization problems

Module content

• Necessary and sufficient conditions of optimality
• Line search
• The gradient method, Newton's method, conjugate direction methods, quasi-Newton methods, methods without derivatives
• Kuhn-Tucker conditions
• Penalty function methods
• Exact methods
• Recursive quadratic programming
• Global optimization

Module lead

Alessandro Astolfi

ECTS/FHEQ

5/7

Module code

ELEC70098

Host department

Department of Electrical and Electronic Engineering

Term

Autumn

Time slot

AM

Teaching weeks

TBC

August resit opportunity?

Yes

How to apply

Please follow these instructions

Application deadline

17.00 on Friday 27 October 2023

Places available (approximate)

No cap

Number of applicants (historic)

223 (2022-23)

Criteria used for student selection

N/A

Further information

EEE Intranet