Time: October 15, 2009, 1100-1125 hours
Place: Erskine 415
Speaker: Josh Collins

Title:
Trans-dimensional Rigourous Global Optimisation

Abstract:
Given some real valued function f a common question to ask is 'where on
the domain does f obtain a maximum/minimum and what is that value?' A
common method utilised is Newton's method applied to the gradient of the
function which may be abstracted to f defined on higher dimensions,
albeit not easily. This talk will discuss how interval arithmetic can
be applied to this problem to obtain bounds on where the extrema may be,
concentrating first on when f has a real valued one dimensional domain,
then noting how to extend this to higher dimensions and further then to
sets of real valued functions on differing domains with possibly
different dimensions, or 'labeled functions'.  The labeled functions play
the role of model-specific likelihood functions in maximum likelihood
estimation.