On a Robust Approach to “split” Feasibility Problems: Solvability and Global Error Bound Conditions

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds are investigated. This is done by reformulating the robust counterpart of a split feasibility problem as a set-valued inclusion, a problem format for which one can take profit from the solvability and stability theory that has been recently developed. As a result, a sufficient condition for solution existence and error bounds is established in terms of problem data and discussed through several examples. A specific focus is devoted to error bound conditions in the case in which the robust counterpart of split feasibility problems is polyhedral. Connections with some of the existent error bound conditions for the original split feasibility problem are also discussed.