An acceleration scheme for solving convex feasibility problems using incomplete projection algorithms

The Projected Aggregation Methods (PAM) for solving linear systems of equalities and/or inequalities, generate a new iterate x(k+1) by projecting the current point x(k) onto a separating hyperplane generated by a given linear combination of the original hyperplanes or half-spaces. In [12] we introduced acceleration schemes for solving systems of linear equations by applying optimization techniques to the problem of finding the optimal combination of the hyperplanes within a PAM like framework. In this paper we generalize those results, introducing a new accelerated iterative method for solving systems of linear inequalities, together with the corresponding theoretical convergence results. In order to test its efficiency, numerical results obtained applying the new acceleration scheme to two algorithms introduced by Garcia-Palomares and Gonzalez-Castano [6] are given.