  We discuss a special form of gradient descent that in the literature has
become known as the so-called linearised Bregman iteration. The idea is to
replace the classical (squared) two norm metric in the gradient descent setting
with a generalised Bregman distance, based on a more general proper, convex and
lower semi-continuous functional. Gradient descent as well as the entropic
mirror descent by Nemirovsky and Yudin are special cases, as is a specific form
of non-linear Landweber iteration introduced by Bachmayr and Burger. We are
going to analyse the linearised Bregman iteration in a setting where the
functional we want to minimise is neither necessarily Lipschitz-continuous (in
the classical sense) nor necessarily convex, and establish a global convergence
result under the additional assumption that the functional we wish to minimise
satisfies the so-called Kurdyka-{\L}ojasiewicz property.
