Abstract
Summary: In this paper we introduce two conceptual algorithms for minimising abstract convex functions. Both algorithms rely on solving a proximal-type subproblem with an abstract Bregman distance based proximal term. We prove their convergence when the set of abstract linear functions forms a linear space. This latter assumption can be relaxed to only require the set of abstract linear functions to be closed under the sum, which is a classical assumption in abstract convexity. We provide numerical examples on the minimisation of nonconvex functions with the presented algorithms.
Type
Reinier Diaz Millan
Lecturer in Mathematics
Julien Ugon
Associate Professor in Mathematics
My research interests include nonsmooth analysis, optimisation and generalised convexity.