We study the common fixed points problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We propose a definition of sparseness of a family of operators and investigate a string-averaging algorithmic scheme that favorably handles the common fixed points problem when the family of operators is sparse. The convex feasibility problem is treated as a special case and a new subgradient projections algorithmic scheme is obtained.
International Transactions in Operational Research, Vol. 16 (2009), pp. 481-494.