Gradient Methods for Problems with Inexact Model of the Objective
Abstract
We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes inexact oracle and relative smoothness condition. We analyze gradient method which uses this inexact model and obtain convergence rates for convex and strongly convex problems. To show potential applications of our general framework we consider three particular problems. The first one is clustering by electorial model introduced in [Nesterov, 2018]. The second one is approximating optimal transport distance, for which we propose a Proximal Sinkhorn algorithm. The third one is devoted to approximating optimal transport barycenter and we propose a Proximal Iterative Bregman Projections algorithm. We also illustrate the practical performance of our algorithms by numerical experiments.
Cite
@article{arxiv.1902.09001,
title = {Gradient Methods for Problems with Inexact Model of the Objective},
author = {Fedor Stonyakin and Darina Dvinskikh and Pavel Dvurechensky and Alexey Kroshnin and Olesya Kuznetsova and Artem Agafonov and Alexander Gasnikov and Alexander Tyurin and César A. Uribe and Dmitry Pasechnyuk and Sergei Artamonov},
journal= {arXiv preprint arXiv:1902.09001},
year = {2019}
}