DISCRETE REGULARIZATION OF OPTIMAL CONTROL PROBLEMS ON ILL-POSED MONOTONE VARIATIONAL INEQUALITIES

The author considers the problem of minimizing an abstract functional which depends on the control and on the solution of an ill-posed variational inequality (v.i.) with a bounded monotone exact operator with the -property (these properties are not needed for approximate operators, nor is the -property in the pseudomonotone case). Solvability of the problem is shown. For its regularization the original v.i. is regularized by means of v.i. with a small step. A number of generalizations are indicated.