Abstract
We consider the Min Max of a functional which is parametrized by t. We show that, under appropriate conditions, the derivative of the Min Max with respect to t is the Min Max with respect to the points solution of the Min Max problem of the derivative of the original functional with respect to t. To illustrate the use of this theorem, we apply it to the control of an elliptic equation with a non-differentiable observation and to a shape optimal design problem.
This research was supported in part by the National Sciences and Engineering Council of Canada Operating Grant A-8730 and a FCAR Grant from the "Ministère de l'Education du Québec".
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© 1987 International Federation for Information Processing
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Delfour, M.C., Zolésio, JP. (1987). Differentiability of a Min Max and application to optimal control and design problems. Part I. In: Lasiecka, I., Triggiani, R. (eds) Control Problems for Systems Described by Partial Differential Equations and Applications. Lecture Notes in Control and Information Sciences, vol 97. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0038754
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DOI: https://doi.org/10.1007/BFb0038754
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