Incomplete projection algorithms for solving the convex feasibility problem (Q1275443)

The aim of the paper is to present a general scheme for the convex feasibility problem and to prove its convergence under mild conditions. The salient features of the proposed scheme are: (a) No exact projections are required. (b) An acceleration factor \(\lambda\) is introduced, which seems to play a fundamental role in improving the quality of convergence for the incomplete projection algorithms. New acceleration techniques are proposed. Preliminary numerical tests are reported on random problems characterized by linear inequalities. The speedup obtained in a multiprocessing environment is remarkable, in some cases being obtained a superlinear speedup.