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A splitting algorithm for dual monotone inclusions involving cocoercive operators. (English) Zbl 1284.47045
This clearly written paper concerns the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. The author revisits the general primal-dual splitting framework proposed by P. L. Combettes and J.-C. Pesquet [Set-Valued Var. Anal. 20, No. 2, 307–330 (2012; Zbl 1284.47043)] in the presence of Lipschitz operators in the context of cocoercive operators. This leads to a new type of splitting techniques and provides a unifying framework for several algorithms which have recently been proposed in the literature. The strategy used in the proof of the main convergence theorem for the author’s splitting algorithm is to reformulate it as a forward-backward splitting algorithm in a real Hilbert space endowed with an appropriate norm. An application to certain minimization problems is also included.

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
49M29 Numerical methods involving duality
49M27 Decomposition methods
90C25 Convex programming
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