The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous gradient. We assume, that the functional constraint can be non-smooth, but satisfying the Lipschitz condition. In particular, such functionals appear in the well-known Truss Topology Design problem. Also we have applied the technique of restarts in the mentioned version of Mirror Descent for strongly convex problems. Some estimations for a rate of convergence are investigated for considered Mirror Descent algorithms.
@article{arxiv.1803.01329,
title = {One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth properties},
author = {Fedor S. Stonyakin and Alexander A. Titov},
journal= {arXiv preprint arXiv:1803.01329},
year = {2018}
}