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A parameterized Douglas–Rachford algorithm

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Abstract

Based on a reparametrization of the Douglas–Rachford algorithm, we provide a principle of finding the least norm solution for a sum of two maximally monotone operators. The algorithm allows us to find the least norm solution to a sum of monotone operators, and even generally to find the least norm primal-dual solution to inclusions with mixtures of composite monotone operators. Three numerical results illustrate our results.

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Acknowledgements

We would like to thank the associate editor and two anonymous referees for suggestions and comments. Dongying Wang was supported by Grants of Xianfu Wang. Xianfu Wang was partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Dongying Wang & Xianfu Wang

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China

    Xianfu Wang

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  1. Dongying Wang
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  2. Xianfu Wang
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Correspondence to Xianfu Wang.

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Wang, D., Wang, X. A parameterized Douglas–Rachford algorithm. Comput Optim Appl 73, 839–869 (2019). https://doi.org/10.1007/s10589-019-00088-8

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  • DOI: https://doi.org/10.1007/s10589-019-00088-8

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