  We propose several adaptive algorithmic methods for problems of non-smooth
convex optimization. The first of them is based on a special artificial
inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of
objective functional in optimization is introduced and some gradient-type
methods with adaptation of inexactness parameters are proposed. A similar
concept of an inexact model is introduced for variational inequalities as well
as for saddle point problems. Analogues of switching sub-gradient schemes are
proposed for convex programming problems with some general assumptions.
