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.
Panicucci, B., Pappalardo, M., Passacantando, M. (2009). A globally convergent descent method for nonsmooth variational inequalities. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 43(2), 197-211 [10.1007/s10589-007-9132-y].
A globally convergent descent method for nonsmooth variational inequalities
Passacantando, M
2009
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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