  In this paper, we consider gradient-type methods for convex positively
homogeneous optimization problems with relative accuracy. An analogue of the
accelerated universal gradient-type method for positively homogeneous
optimization problems with relative accuracy is investigated. The second
approach is related to subgradient methods with B. T. Polyak stepsize. Result
on the linear convergence rate for some methods of this type with adaptive step
adjustment is obtained for some class of non-smooth problems. Some
generalization to a special class of non-convex non-smooth problems is also
considered.
