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arXiv · 2109.06771

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

Luis Briceño-Arias·Fernando Roldán
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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 extend 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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Luis Briceño-Arias, Fernando Roldán. 2021-09-14. Resolvent of the parallel composition and proximity operator of the infimal postcomposition. https://arxiv.org/abs/2109.06771

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