November 05:

2.30-4.00. Ian Coope, University of Canterbury, New Zeland

TITLE: 40 Years of the Nelder-Mead Algorithm

ABSTRACT: The Nelder-Mead algorithm for unconstrained optimization has been used extensively to solve parameter estimation (and other) problems for almost 40 years. Despite its age it is still the method of choice for many practitioners in the fields of statistics, engineering and the physical and medical sciences because it is easy to code and very easy to use. It belongs to a class of methods which do not require derivatives and which are often claimed to be robust for problems with discontinuities or where function values are noisy. However, relatively recently McKinnon showed that the method can converge to non-solutions on certain classes of problems. Only very limited convergence results exist for a restricted class of problems in 1 or 2 dimensions. So why is the method still used? How can it be improved? Recent developments are presented to help answer these questions.