  We consider a general decomposable convex optimization problem. By using
right-hand side allocation technique, it can be transformed into a collection
of small dimensional optimization problems. The master problem is a convex
non-smooth optimization problem. We propose to apply the exact non-smooth
penalty method, which gives a solution of the initial problem under some fixed
penalty parameter and provides the consistency of lower level problems. The
master problem is suggested to be solved by a two-speed subgradient projection
method, which enhances the step-size selection. Preliminary results of
computational experiments confirm its efficiency.
