# On Some Adaptive Mirror Descent Algorithms for Convex and Strongly Convex Optimization Problems with Functional Constraints

arXiv: https://arxiv.org/abs/1812.07639 · HTML: https://mlsanity.com/paper/1812.07639/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [Primal-Dual Stochastic Mirror Descent for MDPs](https://mlsanity.com/paper/2103.00299/) (2021)

## Abstract (arXiv)

In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are applicable to the objective functionals of various level of smoothness: the Lipschitz condition is valid either for the objective functional itself or for its gradient or Hessian (and the functional may not satisfy the Lipschitz condition). By using the restart technique methods for strongly convex minimization problems are proposed. Estimates of the rate of convergence of the considered algorithms are obtained depending on the level of smoothness of the objective functional. Numerical experiments illustrating the advantages of the proposed methods for some examples are presented.