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Programme & Unit Catalogues

## MA40050: Numerical optimisation and large-scale systems

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 2
Assessment Summary: CW 25%, EX 75%
Assessment Detail:
• Coursework (CW 25%)
• Examination (EX 75%)
Supplementary Assessment: MA40050 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20218 AND take MA20222
Description: Aims:
To teach an understanding of iterative methods for nonlinear equations and optimisation.

Learning Outcomes:
Students should know a range of modern iterative methods for solving nonlinear systems and optimisation problems. They should be able to analyse their algorithms and should have an understanding of relevant practical issues and their importance in a range of application areas.

Skills:
Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing.

Content:
Topics will be chosen from the following:
Solution methods for nonlinear equations: Newton's method. Computation of solution paths. Pseudo-arc length continuation.
Unconstrained Optimisation: Line search vs trust region methods. Quasi-Newton and nonlinear conjugate gradient. Linear and nonlinear least squares.
Constrained Optimisation: Optimality conditions, KKT systems, numerical methods for constrained optimisation, linear and nonlinear programming.
Large-scale systems: A motivating example from PDE-constrained optimisation. Reduced-order models (e.g., SVD-based methods) and sparse linear systems (e.g., iterative methods and preconditioners).
Programme availability:

#### MA40050 is Optional on the following programmes:

Department of Mathematical Sciences
• RSMA-AFM16 : Integrated PhD in Statistical Applied Mathematics
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• TSMA-AFM17 : MRes Statistical Applied Mathematics
• TSMA-AFM09 : MSc Mathematical Sciences
• TSMA-APM09 : MSc Mathematical Sciences
• TSMA-AFM08 : MSc Modern Applications of Mathematics
• TSMA-AWM14 : MSc Modern Applications of Mathematics
• TSMA-AFM16 : MSc Statistical Applied Mathematics
• USMA-AFB05 : BSc(Hons) Statistics (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)

Notes:
* This unit catalogue is applicable for the 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.