In this paper, we concentrate on an abstract iterative procedure for solving nonsmooth constrained generalized equations.This procedure employs both the property of weak point-based approximation and the approach of searching for a feasible inexact projection on the constrained set.Utilizing Riding Apparel - Chaps the contraction mapping principle, we establish higher order local convergence of the proposed method under the assumption of metric regularity property which ensures that the iterative procedure generates a sequence converging to a solution of the constrained generalized equation.
Under strong metric regularity assumptions, we obtain that each sequence generated by this procedure converges to a solution.Furthermore, a restricted version of the proposed method is considered, for Cowhides which we establish the desired convergence for each iterative sequence without a strong metric subregularity condition.The obtained results are new even for generalized equations without a constraint set.