Penalty method bounds for variational inequalities with cone constraints

An O() rate of convergence bound is established for a version of the penalty method for variational inequalities in a reflexive Banach space that are associated with a strongly monotone Lipschitz operator and are subject to cone constraints. It is shown that the fictitious domain method can be interpreted as a penalty method, and the corresponding convergence theorems can be deduced from the general penalty-method theorems. An error bound of the Galerkin method for the penalty problem is proved for the case of variational inequalities in a Banach space densely embedded in a Hilbert space. A convergence theorem is given for an iteration process solving the Galerkin-method finite-dimensional problem.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 3–11, 1991.