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Mappings semi-Taylorian from below and sufficient conditions for an extremum. (Russian) Zbl 0741.49007
The paper is closely related to issues considered by V. M. Alekseev, V. M. Tikhomirov and S. V. Fomin [see “Optimal control” (Russian) (1979; Zbl 0516.49002); for a review of the 1987 English translation see Zbl 0689.49001] and by E. S. Levitin, A. A. Miljutin and N. P. Osmolovskij [Usp. Mat. Nauk 33, No. 6(204), 85- 148 (1978; Zbl 0409.49016)]. An analogue of the Taylor expansion for mappings in normed spaces is used to prove second order extremum conditions in extremal problems with equality and inequality constraints. Taylor expansion properties of the Gâteaux functional are studied.

MSC:
49K27 Optimality conditions for problems in abstract spaces
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