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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 6, Pages 32–46 (Mi ivm6943)  
The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control

S. Ya. Serovaiskii

Chair of the Calculus Mathematics, Kazakh National University, Almaty, Republic of Kazakhstan
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Abstract: We consider a control system described by a nonlinear elliptic equation. Its control-state mapping is extended differentiable but not Gateaux differentiable for large values of the domain dimension and the nonlinearity index. We obtain a necessary optimality condition for various state functionals.
Keywords: optimal control, nonlinear elliptic equation, extended differentiability, optimality conditions.
Received: 29.05.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 6, Pages 26–38
DOI: https://doi.org/10.3103/S1066369X10060046
Bibliographic databases:
Document Type: Article
UDC: 571.977
Language: Russian
Citation: S. Ya. Serovaiskii, “The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 6, 32–46; Russian Math. (Iz. VUZ), 54:6 (2010), 26–38
Citation in format AMSBIB
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\paper The necessary optimality conditions for a~nonlinear stationary system whose state functional is not differentiable with respect to the control
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 6
\pages 32--46
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\jour Russian Math. (Iz. VUZ)
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\vol 54
\issue 6
\pages 26--38
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649559202}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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