scholarly journals No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

2007 ◽  
Vol 117 (1-2) ◽  
pp. 21-50 ◽  
Author(s):  
J. Frédéric Bonnans ◽  
Audrey Hermant
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
State Constraint ◽  
Second Order ◽  
Control Problems ◽  
Second Order Optimality Conditions ◽  
Single State ◽  
And Control

scholarly journals Second order optimality conditions for periodic optimal control problems governed by semilinear parabolic differential equations

2021 ◽  
Author(s):  
Hanbing Liu ◽  
Gengsheng Wang
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Second Order ◽  
Order Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Parabolic Differential Equations ◽  
Second Order Optimality Conditions ◽  
Linear Parabolic Equations

In this paper, we study second-order optimality conditions for some optimal control problems governed by some semi-linear parabolic equations with periodic state constraint in time. We obtain a necessary condition and a sufficient condition in terms of the second order derivative of the associated Lagrangian. These two conditions  correspond  to the positive definite and the nonnegativity of the second order derivative of the Lagrangian on the same cone, respectively.

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