Optimisation Geometry

This article demonstrates how an understanding of the geome try of a family of cost functions can be used to develop efficient nume rical algorithms for real-time optimisation. Crucially, it is not the geometry o f 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 nonconvex optimisation problems because none of the cost functions in a family need b convex in order for efficient numerical algorithms to exist for optimising i n 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 distribu tions being called information geometry.

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