Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We present a unifying framework for nonsmooth convex minimization bringing together is an element of-subgradient algorithms and methods for the convex feasibility problem. This development is a natural step for is an element of-subgradient methods in the direction of constrained optimization since the Euclidean projection frequently required in such methods is replaced by an approximate projection, which is often easier to compute. The developments are applied to incremental subgradient methods, resulting in new algorithms suitable to large-scale optimization problems, such as those arising in tomographic imaging.20315471572Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [476825/2004-0, 304820/2006-7]FAPESP [2002/07153-2]