MT3042 Optimisation theory (half course)
MT2116 Abstract mathematics.
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.