This article is cited in 2 papers

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

I. V. Konnov

Kazan State University

Abstract: 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.

UDC: 519.6

Received: 18.02.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:1, 56–63

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