New second order necessary condition for optimal control problems

1986 ◽  
Author(s):  
V. Zeidan ◽  
P. Zezza
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Second Order ◽  
Necessary Condition ◽  
Control Problems

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.

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

Sign in / Sign up

Export Citation Format

Share Document