It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  If we use a decomposition approach in order to solve a minimization problem we often get an objective function in such a w a y that its domain dom 6 = n is not given explicitely to us.  ...  Recently, several homotopy methods, such a s i n terior-point and smoothing methods, have been employed to solve the problem.  ...