Article ID Journal Published Year Pages File Type
840293 Nonlinear Analysis: Theory, Methods & Applications 2013 5 Pages PDF
Abstract

Let H1,H2,H3H1,H2,H3 be real Hilbert spaces, let C⊂H1C⊂H1, Q⊂H2Q⊂H2 be two nonempty closed convex level sets, let A:H1→H3A:H1→H3, B:H2→H3B:H2→H3 be two bounded linear operators. Our interest is in solving the following new convex feasibility problem equation(1.1)Find x∈C,y∈Q such that Ax=By,Find x∈C,y∈Q such that Ax=By, which allows asymmetric and partial relations between the variables xx and yy. In this paper, we present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution of (1.1). The interest of RACQA is that we just need projections onto half-spaces, thus making the relaxed CQ-algorithm implementable. Note that, by taking B=IB=I, in (1.1), we recover the split convex feasibility problem originally introduced in Censor and Elfving (1994) [13] and used later in intensity-modulated radiation therapy (Censor et al. (2006) [11]). We also recover the relaxed CQ-algorithm introduced by Yang (2004) [8] by particularizing both BB and a given parameter.

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