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MA40050: Numerical optimisation and large-scale systems

Follow this link for further information on academic years Academic Year: 2019/0
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 2
Further information on unit assessment Assessment Summary: CW 25%, EX 75%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 25%)
  • Examination (EX 75%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20218 AND take MA20222
Further information on descriptions 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).
Further information on programme availabilityProgramme availability:

MA40050 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFB20 : BSc(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AAB20 : BSc(Hons) Computer Science and Mathematics with Study year abroad (Year 4)
  • USCM-AKB20 : BSc(Hons) Computer Science and Mathematics with Year long work placement (Year 4)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 3)
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 3)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 3)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences
  • RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
  • TSMA-AFM17 : MRes Statistical Applied Mathematics
  • TSMA-AFM08 : MSc Modern Applications of Mathematics
  • TSMA-AFM16 : MSc 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-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)
  • 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)
  • 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)

Notes: