A Splitting Algorithm for System of Composite Monotone Inclusions
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We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resulting algorithm is an extension of the algorithm in Becker and Combettes (J. Convex Nonlinear Anal. 15, 137–159, 2014). The weak convergence of the algorithm proposed is proved. Applications to minimization problems is demonstrated.
KeywordsCoupled system Monotone inclusion Monotone operator Splitting method Lipschitzian operator Forward-backward-forward algorithm Composite operator Duality Primal-dual algorithm
Mathematics Subject Classification (2010)47H05 49M29 49M27 90C25
This work is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 102.01-2014.02. A part of the research work of Dinh Dũng was done when the author was working as a research professor at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and working condition. We thank the referees for their suggestions and corrections which helped to improve the first version of the manuscript.
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