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On String-Averaging for Sparse Problems and On the Split Common Fixed Point Problem

On String-Averaging for Sparse Problems and On the Split Common Fixed Point Problem,Yair Censor,Alexander Segal

On String-Averaging for Sparse Problems and On the Split Common Fixed Point Problem   (Citations: 4)
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We review the common …xed point problem for the class of directed operators. This class is important because many commonly used non- linear operators in convex optimization belong to it. We present our recent de…nition of sparseness of a family of operators and discuss a string-averaging algorithmic scheme that favorably handles the com- mon …xed points problem when the family of operators is sparse. We also review some recent results on the multiple operators split com- mon …xed point problem which requires to …nd a common …xed point of a family of operators in one space whose image under a linear trans- formation is a common …xed point of another family of operators in the image space.
Published in 2008.
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