Abstract
We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments.
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This work has been supported by the National Research Program PRIN/2005017083 “Innovative Problems and Methods in Nonlinear Optimization”.
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Panicucci, B., Pappalardo, M. & Passacantando, M. A globally convergent descent method for nonsmooth variational inequalities. Comput Optim Appl 43, 197–211 (2009). https://doi.org/10.1007/s10589-007-9132-y
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DOI: https://doi.org/10.1007/s10589-007-9132-y