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The paper is devoted to a special Mirror Descent algorithm for problems ofconvex minimization with functional constraints. The objective function may notsatisfy the Lipschitz condition, but it must necessarily have theLipshitz-continuous gradient. We assume, that the functional constraint can benon-smooth, but satisfying the Lipschitz condition. In particular, suchfunctionals appear in the well-known Truss Topology Design problem. Also wehave applied the technique of restarts in the mentioned version of MirrorDescent for strongly convex problems. Some estimations for a rate ofconvergence are investigated for considered Mirror Descent algorithms.

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