Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications

Abstract : 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 Lipschitzian 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 solution 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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SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2013, 23 (4), pp.2420-2447. 〈10.1137/130904160〉
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Soumis le : mercredi 13 mars 2013 - 17:55:18
Dernière modification le : mercredi 21 mars 2018 - 18:56:45

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Patrick Louis Combettes. Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications. SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2013, 23 (4), pp.2420-2447. 〈10.1137/130904160〉. 〈hal-00800511〉

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