Abstract
We prove an existence theorem for the optimal control of variational inequalities governed by a pseudomonotone operator: the cost is assumed to be quadratic. Then, we give an extension of the theorem to more general costs (assuming the operator to be monotone); we also give a result on a perturbation problem.
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Yvon, J. P.,Optimal Control of Systems Governed by Variational Inequalities, Proceedings of the 5th Conference on Optimization Techniques, Part 1, Edited by R. Conti and R. Ruberti, Springer, Berlin, Germany, 1973.
Lions, J. L.,Optimal Control of Systems Governed by Partial Differential Equations, Springer, Berlin, Germany, 1971.
Browder, F. E.,Remarks on the Direct Method of the Calculus of Variations, Archive for Rational Mechanics and Analysis, Vol. 20, pp. 251–258, 1965.
Lions, J. L.,Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, France, 1969.
Duvaut, G., andLions, J. L.,Les Inéquations en Mécanique et en Physique, Dunod, Paris, France, 1972.
Mosco, U.,Convergence of Convex Sets and of Solutions of Variational Inequalities, Advances in Mathematics, Vol. 3, pp. 510–585, 1969.
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Communicated by R. Conti
This work is an extended part of the author's thesis, written under the direction of Professor T. Zolezzi. This research was partially supported by the Consiglio Nazionale delle Ricerche (CNR), Rome, Italy.
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Patrone, F. On the optimal control for variational inequalities. J Optim Theory Appl 22, 373–388 (1977). https://doi.org/10.1007/BF00932861
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DOI: https://doi.org/10.1007/BF00932861