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The sequential differentiation and its applications in the optimal control problems. (English. Russian original) Zbl 1180.49016
Russ. Math. 52, No. 7, 38-47 (2008); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2008, No. 7, 45-46 (2008).
Summary: Using the sequential approach, we define a certain generalization of the operator derivative. We establish the necessary extremum condition in terms of the sequential derivative. As examples we consider the optimal control problems for systems governed by partial nonlinear differential equations of several kinds.
MSC:
49J52 Nonsmooth analysis
49K20 Optimality conditions for problems involving partial differential equations
46G05 Derivatives of functions in infinite-dimensional spaces
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