Optimisation Geometry
Abstract
This article demonstrates how an understanding of the geometry of a family of cost functions can be used to develop efficient numerical algorithms for real-time optimisation. Crucially, it is not the geometry of the individual functions which is studied, but the geometry of the family as a whole. In some respects, this challenges the conventional divide between convex and non-convex optimisation problems because none of the cost functions in a family need be convex in order for efficient numerical algorithms to exist for optimising in real-time any function belonging to the family. The title "Optimisation Geometry" comes by analogy from the study of the geometry of a family of probability distributions being called information geometry.
Cite
@article{arxiv.1212.1775,
title = {Optimisation Geometry},
author = {Jonathan H. Manton},
journal= {arXiv preprint arXiv:1212.1775},
year = {2012}
}
Comments
14 pages