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Resolvent of the parallel composition and the proximity operator of the infimal postcomposition

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Abstract

In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild assumptions. Connections with a modification of the warped resolvent are provided. In the context of convex optimization, we obtain the proximity operator of the infimal postcomposition of a convex function by a linear operator and we relax full range conditions on the linear operator to mild qualification conditions. We also introduce a generalization of the proximity operator involving a general linear bounded operator leading to a generalization of Moreau’s decomposition for composite convex optimization.

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Acknowledgements

The first author thanks the support of ANID under grants FONDECYT 1190871, Centro de Modelamiento Matemático (CMM) FB210005 BASAL funds for centers of excellence, and grant Redes 180032. The second author thanks the support of ANID-Subdirección de Capital Humano/Doctorado Nacional/2018-21181024 and of the Dirección de Postgrado y Programas from UTFSM through Programa de Incentivos a la Iniciación Científica (PIIC).

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  1. Universidad Técnica Federico Santa María, Santiago, Chile

    Luis M. Briceño-Arias & Fernando Roldán

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  1. Luis M. Briceño-Arias
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  2. Fernando Roldán
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Correspondence to Luis M. Briceño-Arias.

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Briceño-Arias, L.M., Roldán, F. Resolvent of the parallel composition and the proximity operator of the infimal postcomposition. Optim Lett 17, 399–412 (2023). https://doi.org/10.1007/s11590-022-01906-5

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  • DOI: https://doi.org/10.1007/s11590-022-01906-5

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