Unification of basic and composite nondifferentiable optimization

There are two main classes of iterative methods in nondifferentiable optimization (NDO). In the basic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in the composite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. The present work unifies these two approaches for benefiting of their respective advantages.