Geodesic
A nonlinear descent method for a~variational inequality on a~nonconvex set
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2009), pp. 66-75

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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.
Keywords: generalized variational inequality, nonsmooth mapping, nonlinear descent method. 
@article{IVM_2009_1_a2,
     author = {I. V. Konnov},
     title = {A nonlinear descent method for a~variational inequality on a~nonconvex set},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {66--75},
     publisher = {mathdoc},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_1_a2/}
}
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I. V. Konnov. A nonlinear descent method for a~variational inequality on a~nonconvex set. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2009), pp. 66-75. http://geodesic.mathdoc.fr/item/IVM_2009_1_a2/