A nonlinear descent method for a variational inequality on a nonconvex set

In this paper, we consider a generalized variational inequality problem which involves the integrable cost mapping and a nonsmooth mapping with convex components. We propose a new gradient type method, which determines a stepsize by using the smooth part of the cost function. Thus, the method does not utilize analogs of derivatives of non-smooth functions. We show that its convergence does not require additional assumptions.