We prove an existence theorem of Lagrange multipliers for an abstract control problem in Banach spaces. This theorem may be applied to obtain optimality conditions for control problems governed by partial differential equations in the presence of pointwise state constraints.
Publié le : 1998-07-04
Classification:
Optimal control,
Optimality conditions,
Lagrange multipliers in Banach spaces,
Karush\-Kuhn\-Tucker type theorems,
Inequality constraints in Banach spaces,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-00993908,
author = {Alibert, Jean-Jacques and Raymond, Jean-Pierre},
title = {A lagrange multiplier theorem for control problems with state constraints},
journal = {HAL},
volume = {1998},
number = {0},
year = {1998},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00993908}
}
Alibert, Jean-Jacques; Raymond, Jean-Pierre. A lagrange multiplier theorem for control problems with state constraints. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-00993908/