Abstract
Iterative numerical algorithms for variational inequalities are systematically constructed from fixed-point problem characterizations in terms of resolvent operators. The applied method is the one introduced by Gabay in [Ga], used here in the context of discrete variational inequalities, and with the emphasis on mixed finite element models. The algorithms apply to nonnecessarily potential problems, generalizing primal and mixed Uzawa and augmented Lagrangian-type algorithms. They are also identified with Euler and operator splitting methods for the time discretization of evolution first-order problems.
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Communicated by R. Temam
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Alduncin, G. On Gabay’s algorithms for mixed variational inequalities. Appl Math Optim 35, 21–44 (1997). https://doi.org/10.1007/BF02683318
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DOI: https://doi.org/10.1007/BF02683318
Key Words
- Proximal-point algorithms
- Operator-splitting methods
- Variational inequalities
- Initial and boundary-value constrained problems
- Mixed finite elements