THE SUBGRADIENT METHOD FOR SOLVING VARIATIONAL INEQUALITIES WITH COMPUTATIONAL ERRORS IN A HILBERT SPACE

Abstract

In a Hilbert space, we study the asymptotic behavior of the subgradient method for solving a variational inequality, under the presence of computational errors. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method to the solution of a variational inequalities is established for nonsummable computational errors. We show that the the subgradient method generates good approximate solutions, if the sequence of computational errors is bounded from above by a constant.