scholarly journals Analysis and finite element approximations of stochastic optimal control problems constrained by stochastic elliptic partial differential equations

2008 ◽  
Author(s):  
Jangwoon Lee
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Elliptic Partial Differential Equations ◽  
Control Problems ◽  
Partial Differential ◽  
Finite Element Approximations

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.

scholarly journals Optimal control of nonsmooth system governed by quasi-linear elliptic equations

1997 ◽  
Vol 20 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Gong Liutang ◽  
Fei Pusheng
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Original Problem ◽  
Optimal Control Problems ◽  
Elliptic Partial Differential Equations ◽  
Necessary Condition ◽  
Control Problems ◽  
Nonsmooth Systems

In this paper, we discuss a class of optimal control problems of nonsmooth systems governed by quasi-linear elliptic partial differential equations, give the existence of the problem. Through the smoothness and the approximation of the original problem, we get the necessary condition, which can be considered as the Euler-Lagrange condition under quasi-linear case.

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