The penalty method for variational ineqalities with nonsmooth unbounded operators in banach space
Ya. I. Alber · Numerical Functional Analysis and Optimization · 1995
In this paper we study the existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach space. All the objects of the inequality-the operator, “the data” and the set of constraints-are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the space and its dual. The results of this paper extend and generalize results of Lions [13]. They are new even in Hilbert spaces.