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On the String Averaging Method for Sparse Common Fixed Points Problems

Yair Censor (yair***at***math.haifa.ac.il)
Alexander Segal (asegal***at***math.haifa.ac.il)

Abstract: We study the common fixed points problem for the class of directed operators. This class is important because many commonly used nonlinear operators in convex optimization belong to it. We propose a definition of sparseness of a family of operators and investigate a string-averaging algorithmic scheme that favorably handles the common fixed points problem when the family of operators is sparse. The convex feasibility problem is treated as a special case and a new subgradient projections algorithmic scheme is obtained.

Keywords: Common fixed points, directed operators, string-averaging algorithmic scheme, sparseness.

Category 1: Convex and Nonsmooth Optimization (Other )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: International Transactions in Operational Research, Vol. 16 (2009), pp. 481-494.

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Entry Submitted: 08/02/2008
Entry Accepted: 08/02/2008
Entry Last Modified: 07/06/2009

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