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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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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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
- Maximal monotone operators
- State-dependent variational inclusion
- Douglas–Rachford splitting algorithm
- Quasivariational inequalities