We present a framework for analyzing convergence and local rates of convergence of a class of descent algorithms, assuming the objective function is weakly convex. The framework is general, in the sense that it combines the possibility of explicit iterations (based on the gradient or a subgradient at the current iterate), implicit iterations (using a … Read more
Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of … Read more
We study the iterate convergence of strong descent algorithms applied to convex functions. We assume that the function satisfies a very simple growth condition around its minimizers, and then show that the trajectory described by the iterates generated by any such method has finite length, which proves that the sequence of iterates converge. Citation Federal … Read more
In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Lojasiewicz inequality. This assumption allows to cover a … Read more