A CONJECTURE BY DE PIERRO IS TRUE FOR TRANSLATES OF REGULAR SUBSPACES

摘要: Suppose we are given nitely many nonempty closed convex sets in a real Hilbert space and their associated projections. For suitable arrangements of the sets, it is known that sequence obtained by iterating composi- tion underrelaxed projections weakly convergent. The question arises how these weak limits vary as underrelaxation parameter tends to zero. In 2001, De Pierro conjectured approach least squares so- lution nearest starting point sequence. fact, result Censor, Eggermont, Gordon implies Pierro's conjecture for ane subspaces Euclidean space. This paper extends Censor et al. from We show true translates regular all exist with respect norm topology. Regularity always holds However, this condition not automatic innite-dimension al Two constructed illustrate possible divergence iterates composition Somewhat surprisingly, examples plane demonstrate solution can be nonlinear.