Optimization methods adaptive tо «significant» dimension of the problem

Two methods of solving convex, including nonsmooth, problems adapting to the «true» dimension of the problem. The method insure a relatively low labour consumption for solution of problems with a «small number of significant variables». Also, the order of the quaranteed estimate of labour consuming methods on the class of all convex problems, including those for which «all variables are significant» is equal to the potentially feasible one.