One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth properties

Fedor S. Stonyakin; Alexander A. Titov

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arXiv · 1803.01329

One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth properties

Fedor S. Stonyakin·Alexander A. Titov

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Abstract

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.

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BibTeX RIS

Fedor S. Stonyakin, Alexander A. Titov. 2018-03-04. One Mirror Descent Algorithm for Convex Constrained Optimization Problems with non-standard growth properties. https://arxiv.org/abs/1803.01329

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