Prof Bernhard von Stengel COL 4.12

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Mathematical Methods (MA100) and Introduction to Abstract Mathematics (MA103) are pre-requisites. Real Analysis (MA203) is desirable, and students who have not done MA203 should contact the teacher responsible.

The course describes various techniques of optimisation, gives a mathematical presentation of the relevant theory, and shows how they can be applied. Introduction and review of relevant mathematical background Introduction to combinatorial optimisation; shortest paths in directed graphs; algorithms and their running time. Classical results on continuous optimisation: Weierstrass's Theorem on continuous functions on compact set; optimisation of differentiable functions on open sets; Lagrange's Theorem on equality constrained optimisation; Kuhn and Tucker's Theorem on inequality constrained optimisation. Linear programming and duality theory. Finite horizon dynamic programming (time permitting).

22 hours of lectures and 10 hours of classes in the LT.

Written answers to set problems will be expected on a weekly basis.

Information on important and required texts will be provided at the beginning of the course. Good sources of literature are R K Sundaram, A First Course in Optimisation Theory; N L Biggs, Discrete Mathematics (2nd edition). Additional notes will be handed out throughout the course.

Exam (100%, duration: 2 hours) in the main exam period.