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MA264 Content

Aims: The module gives an introduction to the theory of optimisation as well as the fundamentals of approximation theory.


  1. Recap: necessary and sufficient conditions for local min/max, convex functions and sets, Jensen’s inequality, level sets
  2. Iterative algorithms: gradient descent and line search methods
  3. Newton's method
  4. Linear programming with applications in economics and data science
  5. Constrained optimisation
  6. Introduction to Neural Networks
  7. Approximation theory: polynomial approximation, rational approximation, trigonometric approximation
  8. Discrete Fourier and Cosine Transform with applications in imaging and signal processing
  9. Introduction to Wavelets


  • Understand critical points of multivariable functions
  • Apply various techniques to solve nonlinear optimisation problems and understand their applications, in economics and data science
  • Use Lagrange multipliers and the Karush–Kuhn–Tucker conditions to solve constrained nonlinear optimisation problems
  • Understand the basic concepts of approximation theory
  • Obtain an understanding of different approximation techniques used in the digital sciences


  • Endre Sueli and David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003
  • S. Boyd, Convex Optimization, Cambridge University Press, 2004
  • J. D. Powell, Approximation Theory and Methods, Cambridge University Press, 1981
  • N. Trefethen, Approximation Theory and Practice