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Journal Articles SIAM Journal on Optimization Year : 2013

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

Patrick Louis Combettes
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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.

Dates and versions

hal-00800511 , version 1 (13-03-2013)

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Patrick Louis Combettes. Systems of Structured Monotone Inclusions: Duality, Algorithms, and Applications. SIAM Journal on Optimization, 2013, 23 (4), pp.2420-2447. ⟨10.1137/130904160⟩. ⟨hal-00800511⟩
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