Relaxed outer projections,weighted averages and convex feasibility

A new algorithmic scheme is proposed for finding a common point of finitely many closed convex sets. The scheme uses weighted averages (convex combinations) of relaxed projections onto approximating halfspaces. By varying the weights we generalize Cimmino's and Auslender's methods as well as more recent versions developed by Iusem & De Pierro and Aharoni & Censor. Our approach offers great computational flexibility and encompasses a wide variety of known algorithms as special instances. Also, since it is block-iterative, it lends itself to parallel processing.The research of the first author was partially supported by Ruhrgas under a NAVF grant.