A method for solving semi-coercive variational inequalities based on the method of iterative proximal regularization (Q2387068)

The authors consider the usual proximal point method in a Hilbert space \(H=H_{1}+H_{2}\), where \(H_{1}\) is finite-dimensional, applied to minimization of a convex function \(\gamma\) over a convex closed subset in \(H\). The function \(\gamma\) is supposed to be strongly convex in the subspace \(H_{2}\). Such methods were considered by \textit{A. A. Kaplan} [Tr. Inst. Mat. 10, 132--159 (1988; Zbl 0671.49037)]. The authors prove the strong convergence of the method and describe its application to an elasticity theory problem with friction.