Abstract
We consider infinite dimensional nonlinear programming problem minimize {ino(u) : f(u) ε Y, u ε U} where U is a complete metric space, fo : U → IR, f : U → E are respectively lower semicontinuous and continuous functions, E is a Hilbert space and Y is a closed subset of E . We prove necessary conditions for minima which in the finite dimensional case reduce to Kuhn-Tucker conditions. As an application of these necessary conditions we derive Pontriagin's maximum principle for a class of control systems described by quasilinear equations in a Hilbert space.
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© 1988 Springer-Verlag
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Fattorini, H.O., Frankowska, H. (1988). Necessary conditions for infinite dimensional control problems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042230
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DOI: https://doi.org/10.1007/BFb0042230
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