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We propose a nonsmooth trust-region method for solving optimization problemswith locally Lipschitz continuous functions, with application to problemsconstrained by variational inequalities of the second kind. Under suitableassumptions on the model functions, convergence of the general algorithm to aC-stationary point is verified. For variational inequality constrainedproblems, we are able to properly characterize the Bouligand subdifferential ofthe reduced cost function and, based on that, we propose a computabletrust-region model which fulfills the convergence hypotheses of the generalalgorithm. The article concludes with the experimental study of the mainproperties of the proposed method based on two different numerical instances.

A non-smooth trust-region method for locally Lipschitz functions with application to optimization problems constrained by variational inequalities