Abstract
A variant of the Newton method for nonsmooth equations is applied to solve numerically quasivariational inequalities with monotone operators. For this purpose, we investigate the semismoothness of a certain locally Lipschitz operator coming from the quasi-variational inequality, and analyse the generalized Jacobian of this operator to ensure local convergence of the method. A simplified variant of this approach, applicable to implicit complementarity problems, is also studied. Small test examples have been computed.
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This work has been supported in parts by a grant from the German Scientific Foundation and by a grant from the Czech Academy of Sciences.
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Outrata, J.V., Zowe, J. A Newton method for a class of quasi-variational inequalities. Comput Optim Applic 4, 5–21 (1995). https://doi.org/10.1007/BF01299156
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DOI: https://doi.org/10.1007/BF01299156