APPROXIMATION RESULTS FOR SOLUTION OF STOCHASTIC HARD-SOFT CONSTRAINED CONVEX FEASIBILITY PROBLEM

Abstract

In this work, a random-type iterative scheme is proposed and used for random approximation of the solution of stochastic convex feasibility problem involving hard constraints (that must be satisfied) and soft constraints (whose proximity function is minimized) in Hilbert space. The iterative algorithm is based on an alternating projection with lipschitzian and firmly non-expansive mapping. Convergence results of the random-type iterative scheme to the solution of the stochastic convex feasibility problem is proved. These will serve as an extension, unification and generalization of different established classic results in the literature.