scholarly journals Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems

2015 ◽  
Vol 44 (1) ◽  
pp. 181-202 ◽  
Author(s):  
Eduardo Casas ◽  
Fredi Tröltzsch
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Second Order ◽  
Control Problems ◽  
Second Order Optimality Conditions ◽  
Local Solutions ◽  
Parabolic Optimal 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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