Geodesic
Sufficient optimality conditions for extremal controls based on functional increment formulas
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 96-102.

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We consider optimal control problem without terminal constraints. With the help of nonstandard functional increment formulas we introduce definitions of strongly extremal controls. Such controls are optimal in linear and quadratic problems. In general case, an optimality property is provided with concavity condition of Pontryagin's function with respect to phase variables.
Keywords: optimal control problem, the maximum principle, sufficient optimality conditions. 
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V. A. Srochko; V. G. Antonik. Sufficient optimality conditions for extremal controls based on functional increment formulas. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2014), pp. 96-102. http://geodesic.mathdoc.fr/item/IVM_2014_8_a10/

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