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Optimisation theory MT3042

Half course

This half course brings together several parts of the wide area of mathematical optimisation, as encountered in many applied fields. The emphasis is on the mathematical ideas and theory used in continuous optimisation.

Prerequisite

If taken as part of a BSc degree, courses which must be passed before this half course may be attempted:

  • MT2116 Abstract mathematics.

Students are also strongly encouraged to take MT3041 Advanced mathematical analysis.

Topics covered

This course aims to bring together several parts of the wide area of mathematical optimisation, as encountered in many applied fields.

The course concentrates on continuous optimisation, and in this sense extends the theory studied in standard calculus courses.

In contrast to the Mathematics 1 and Mathematics 2 half courses, the emphasis in this Optimisation Theory course will be on the mathematical ideas and theory used in continuous optimisation. This course covers the following topics:

  • Introduction and review of relevant parts from real analysis, with emphasis on higher dimensions.
  • Weierstrass’ Theorem on continuous functions on compact set.
  • Review with added rigour of unconstrained optimisation of differentiable functions.
  • Lagrange’s Theorem on equality constrained optimisation.
  • The Kuhn-Tucker Theorem on inequality constrained optimisation.
  • Finite and infinite horizon dynamic programming.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Have knowledge and understanding of important definitions, concepts and results in the subject, and of how to apply these in different situations
  • Have knowledge of basic techniques and methodologies in the topics covered
  • Have basic understanding of the theoretical aspects of the concepts and methodologies covered
  • Be able to understand new situations and definitions, including combinations with elements from different areas covered in the course, investigate their properties, and relate them to existing knowledge
  • Be able to think critically and with sufficient mathematical rigour
  • Be able to express arguments clearly and precisely

Assessment

Unseen written examination (2 hrs). 

Essential reading

  • Sundaram, R.K. A First Course in Optimization Theory. Cambridge University Press.

Course information sheets

Download the course information sheets from the LSE website.