Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems

P. 133–149.

Titov A., Stonyakin F. S., Alkousa M., Ablaev S. A., Gasnikov A.

Recently some specific classes of non-smooth and non-Lipsch-itz convex optimization problems were considered by Yu. Nesterov and 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.

Keywords: Convex programming problem, Switching subgradient scheme, Relative lipschitz-continuity, Inexact model, Stochastic mirror descent, Online optimization problem

In book

Mathematical Optimization Theory and Operations Research. 19th International Conference, MOTOR 2020, Novosibirsk, Russia, July 6–10, 2020, Revised Selected Papers

Vol. 1275: Communications in Computer and Information Science . , Springer, 2020.