  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.
