Title: A stroll in the jungle of error bounds,
Abstract: The aim of this paper is to give a short overview on error bounds and to
provide the first bricks of a unified theory. Inspired by the works of [8, 15,
13, 16, 10], we show indeed the centrality of the Lojasiewicz gradient
inequality. For this, we review some necessary and sufficient conditions for
global/local error bounds, both in the convex and nonconvex case. We also
recall some results on quantitative error bounds which play a major role in
convergence rate analysis and complexity theory of many optimization methods.