Continuation for parametrized nonlinear variational inequalities (Q1120256)

Considered is a class of variational inequalities of the type \(u\in V:\) \(f'(u)(v-u)\geq \lambda g'(g)(v-u)\) for all \(v\in V\). Here, V is a closed convex subset of a real Hilbert space H, and \(\lambda\) is a real parameter. \(f'\) and \(g'\) denote respectively the Gǎteaux derivatives of real functionals f and g defined on H. Instead of \(\lambda\), the authors introduce a new continuation parameter, namely the value of the functional f(u) as was done by \textit{H. Beckert} [Math. Nachr. 49, 311-341 (1971; Zbl 0228.49001)] in the case of variational equations. The method of Beckert has been adapted by the authors to variational inequalities. In the present paper, a short outline of the theory is given, and numerical results are presented.