Geodesic
Discrete regularization of optimal control problems on ill-posed monotone variational inequalities
Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 321-335

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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 $\mu$-property (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. 
@article{IM2_1991_37_2_a3,
     author = {O. A. Liskovets},
     title = {Discrete regularization of optimal control problems on ill-posed monotone variational inequalities},
     journal = {Izvestiya. Mathematics },
     pages = {321--335},
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a3/}
}
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O. A. Liskovets. Discrete regularization of optimal control problems on ill-posed monotone variational inequalities. Izvestiya. Mathematics , Tome 37 (1991) no. 2, pp. 321-335. http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a3/