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Modified Projection Algorithms for Solving the Split Equality Problems

The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively an...

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Detalles Bibliográficos
Autores principales: Dong, Qiao-Li, He, Songnian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3916110/
https://www.ncbi.nlm.nih.gov/pubmed/24574882
http://dx.doi.org/10.1155/2014/328787
Descripción
Sumario:The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.