Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems

In the present paper, we use subgradient projection algorithms for solving convex feasibility problems. We show that almost all iterates, generated by a subgradient projection algorithm in a Hilbert space, are approximate solutions. Moreover, we obtain an estimate of the number of iterates which are not approximate solutions. In a finite-dimensional case, we study the behavior of the subgradient projection algorithm in the presence of computational errors. Provided computational errors are bounded, we prove that our subgradient projection algorithm generates a good approximate solution after a certain number of iterates.