Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems
Optimization and Control
2021-05-07 v6
Abstract
Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective function and functional constraints. We introduce a new concept of an inexact model and propose some analogues of switching subgradient schemes for convex programming problems for the relatively Lipschitz-continuous objective function and functional constraints. Some class of online convex optimization problems is considered. The proposed methods are optimal in the class of optimization problems with relatively Lipschitz-continuous objective and functional constraints.
Cite
@article{arxiv.2003.09147,
title = {Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems},
author = {Alexander Titov and Fedor Stonyakin and Mohammad Alkousa and Seydamet Ablaev and Alexander Gasnikov},
journal= {arXiv preprint arXiv:2003.09147},
year = {2021}
}