This paper investigates the problem of minimizing a smooth function over a compact set with a probabilistic relative-error gradient oracle. The oracle succeeds with some probability, in which case it provides a relative-error approximation of the true gradient, or fails and returns an arbitrary vector, while the optimizer cannot distinguish between successful and failed queries … Read more
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters … 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