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 mu-proeprty (these properties are not needed for approximate operators, nor is the mu-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.