We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact (δ,Δ,L)-model of objective functional in optimization is introduced and some gradient-type methods with adaptation of inexactness parameters are proposed. A similar concept of an inexact model is introduced for variational inequalities as well as for saddle point problems. Analogues of switching sub-gradient schemes are proposed for convex programming problems with some general assumptions.
@article{arxiv.1911.08425,
title = {Adaptive Gradient Methods for Some Classes of Non-Smooth Optimization Problems},
author = {Fedor Stonyakin},
journal= {arXiv preprint arXiv:1911.08425},
year = {2020}
}