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Douglas–Rachford splitting algorithm for solving state-dependent maximal monotone inclusions

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Abstract

In this paper, we provide a new application of the Douglas–Rachford splitting method for finding a zero of the sum of two maximal monotone operators where one of them depends implicitly on the state variable. Our proposed algorithms are much simpler with better rate of convergence than existing results and can be implemented under general conditions. Applications to generalized Nash games and quasivariational inequalities are provided. Numerical experiments are also given to illustrate the convergence rate of the proposed algorithms.

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Acknowledgements

The authors would like to thank the referee for insightful comments and suggestions. In particular, B. K. Le wants to express his gratitude to the University of O’Higgins, Chile where some parts of this work were done.

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Authors and Affiliations

  1. XLIM UMR-CNRS 7252, Université de Limoges, 87060, Limoges, France

    S. Adly

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    B. K. Le

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  1. S. Adly
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Correspondence to B. K. Le.

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Adly, S., Le, B.K. Douglas–Rachford splitting algorithm for solving state-dependent maximal monotone inclusions. Optim Lett 15, 2861–2878 (2021). https://doi.org/10.1007/s11590-021-01718-z

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