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The paper is devoted to new modifications of recently proposed adaptivemethods of Mirror Descent for convex minimization problems in the case ofseveral convex functional constraints. Methods for problems of two classes areconsidered. The first type of problems with Lipschitz-continuous objective(generally speaking, nonsmooth) functional. The second one is for problems witha Lipschitz-continuous gradient of the objective smooth functional. We considerthe class of problems with a non-smooth objective functional equal to themaximum of smooth functionals with a Lipschitz-continuous gradient. Note thatfunctional constraints, generally speaking, are non-smooth andLipschitz-contionuous. The proposed modifications allow saving the algorithmrunning time due to consideration of not all functional constraints onnon-productive steps. Estimates for the rate of convergence of the methodsunder consideration are obtained. The methods proposed are optimal from thepoint of view of lower oracle estimates. The results of numerical experimentsillustrating the advantages of the proposed procedure for some examples aregiven.

Adaptive algorithms for mirror descent in convex programming problems with Lipschitz constraints