  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.
