MA40050: Numerical optimisation and largescale systems
[Page last updated: 27 September 2022]
Academic Year:  2022/23 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
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: 
 Likeforlike reassessment (where allowed by programme regulations)

Requisites: 
Before taking this module you must take MA20218 AND take MA20222

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.

Aims:  To teach an understanding of iterative methods for nonlinear equations and optimisation.

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. Pseudoarc length continuation.
Unconstrained Optimisation: Line search vs trust region methods. QuasiNewton and nonlinear conjugate gradient. Linear and nonlinear least squares.
Constrained Optimisation: Optimality conditions, KKT systems, numerical methods for constrained optimisation, linear and nonlinear programming.
Largescale systems: A motivating example from PDEconstrained optimisation. Reducedorder models (e.g., SVDbased methods) and sparse linear systems (e.g., iterative methods and preconditioners).

Programme availability: 
MA40050 is Optional on the following programmes:
Department of Computer Science
 USCMAFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
 USCMAAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
 USCMAKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
 USCMAFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
 USCMAAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
 USCMAKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences
 RSMAAFM16 : Integrated PhD Statistical Applied Mathematics
 TSMAAFM17 : MRes Statistical Applied Mathematics
 TSMAAFM19 : MSc Mathematics with Data Science for Industry
 TSMAAWM19 : MSc Mathematics with Data Science for Industry
 TSMAAFM16 : MSc Statistical Applied Mathematics
 USMAAFB15 : BSc(Hons) Mathematical Sciences (Year 3)
 USMAAAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
 USMAAKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
 USMAAFB13 : BSc(Hons) Mathematics (Year 3)
 USMAAAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
 USMAAFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
 USMAAAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
 USMAAKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
 USMAAFB05 : BSc(Hons) Statistics (Year 3)
 USMAAAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
 USMAAKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
 USMAAFM14 : MMath(Hons) Mathematics (Year 3)
 USMAAFM14 : MMath(Hons) Mathematics (Year 4)
 USMAAAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
 USMAAKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:  This unit catalogue is applicable for the 2022/23 academic year only. Students continuing their studies into 2023/24 and beyond should not assume that this unit will be available in future years in the format displayed here for 2022/23.
 Programmes and units are subject to change 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 prerequisite rules.
 Find out more about these and other important University terms and conditions here.
