Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications
Résumé
A general primal-dual splitting algorithm for solving systems of structured coupled monotone inclusions in Hilbert spaces is introduced and its asymptotic behavior is analyzed. Each inclusion in the primal system features compositions with linear operators, parallel sums, and Lip-schitzian operators. All the operators involved in this structured model are used separately in the proposed algorithm, most steps of which can be executed in parallel. This provides a flexible solu-tion method applicable to a variety of problems beyond the reach of the state-of-the-art. Several applications are discussed to illustrate this point.
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