Strong convergence of almost simultaneous block-iterative projection methods in Hilbert spaces

Abstract We prove strong convergence of a class of block-iterative projection methods for finding a common point of a finite family of closed convex subsets in a Hilbert space.

[1]  Y. Censor,et al.  Block-iterative projection methods for parallel computation of solutions to convex feasibility problems , 1989 .

[2]  Guy Pierra,et al.  Decomposition through formalization in a product space , 1984, Math. Program..

[3]  Dan Butnariu,et al.  Convergence criteria for generalized gradient methods of solving locally Lipschitz feasibility problems , 1992, Comput. Optim. Appl..

[4]  Henry Stark,et al.  Learning in neural nets using projection methods , 1991, Optical Society of America Annual Meeting.

[5]  Boris Polyak,et al.  The method of projections for finding the common point of convex sets , 1967 .

[6]  J. Neumann.  On Rings of Operators. Reduction Theory , 1949 .

[7]  L. Bregman.  The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming , 1967 .

[8]  Yair Censor,et al.  On the behavior of a block-iterative projection method for solving convex feasibility problems , 1990, Int. J. Comput. Math..

[9]  Yair Censor.  On variable block algebraic reconstruction techniques , 1991 .

[10]  N. Ottavy.  Strong convergence of projection-like methods in Hilbert spaces , 1988 .

[11]  Alfredo N. Iusem,et al.  Convergence results for an accelerated nonlinear cimmino algorithm , 1986 .

[12]  H. Trussell,et al.  Method of successive projections for finding a common point of sets in metric spaces , 1990 .

[13]  J. Zowe,et al.  Relaxed outer projections, weighted averages and convex feasibility , 1990 .

[14]  Howard L. Weinert,et al.  Error bounds for the method of alternating projections , 1988, Math. Control. Signals Syst..