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

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.

UDC: 571.977

Received: 29.05.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:6, 26–38

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