2014/05/31 by Pierre Frankel, Guillaume Garrigos, Juan Peypouquet · 1 citation
Mathematics · #math.OC
paper · pdf · doi:10.1007/s10957-014-0642-3
arxiv created 2014/07/07 · arxiv updated 2017/07/14
We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method with variable metric and relative errors. As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailled.