@article{COCV_2000__5__45_0,
author = {Bergounioux, Ma{\"\i}tine and Mignot, Fulbert},
title = {Optimal control of obstacle problems : existence of {Lagrange} multipliers},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {45--70},
year = {2000},
publisher = {EDP Sciences},
volume = {5},
mrnumber = {1745686},
zbl = {0934.49008},
language = {en},
url = {https://www.numdam.org/item/COCV_2000__5__45_0/}
}
TY - JOUR AU - Bergounioux, Maïtine AU - Mignot, Fulbert TI - Optimal control of obstacle problems : existence of Lagrange multipliers JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2000 SP - 45 EP - 70 VL - 5 PB - EDP Sciences UR - https://www.numdam.org/item/COCV_2000__5__45_0/ LA - en ID - COCV_2000__5__45_0 ER -
%0 Journal Article %A Bergounioux, Maïtine %A Mignot, Fulbert %T Optimal control of obstacle problems : existence of Lagrange multipliers %J ESAIM: Control, Optimisation and Calculus of Variations %D 2000 %P 45-70 %V 5 %I EDP Sciences %U https://www.numdam.org/item/COCV_2000__5__45_0/ %G en %F COCV_2000__5__45_0
Bergounioux, Maïtine; Mignot, Fulbert. Optimal control of obstacle problems : existence of Lagrange multipliers. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 45-70. https://www.numdam.org/item/COCV_2000__5__45_0/
[1] , and , Optimal control of variational inequalities. Appl. Math. Optim. 38 ( 1998) 121-140. | Zbl | MR
[2] , Optimal control of variational inequalities. Pitman, Boston, Res. Notes Math. 100 ( 1984). | Zbl | MR
[3] , Optimal control of an obstacle problem. Appl. Math. Optim. 36 ( 1997) 147-172. | MR
[4] , Optimal control of problems governed by abstract variational inequalities with state constraints. SIAM J. Control Optim. 36 ( 1998) 273-289. | Zbl | MR
[5] , Augmented lagrangian method for distributed optimal control problems with state constraints. J. Optim. Theory Appl. 78 ( 1993) 493-521. | Zbl | MR
[6] and , Optimal control of problems governed by obstacle type variational inequalities: A dual regularization-penalization approach. J. Convex Anal. 5 ( 1998) 329-351. | Zbl | MR
[7] , , and , A comparison of interior point methods and a Moreau-Yosida based active set strategy for constrained optimal control problems. Report 98-15 Université d'Orléans ( 1998).
[8] and , Pontryagin principle for problems governed by parabolic variational inequalities. SIAM J. Control Optim. 37 ( 1999) 1273-1290. | Zbl | MR
[9] and , Optimal control of variational inequalities. Optimality conditions and numerical methods. Collection Free Boundary Problems, Application and Theory, Vol. IV. Maubusson, Res. Notes Math. 121 ( 1984) 478-487. | MR
[10] and , Optimal control of a Signorini Problem. SIAM J. Control Optim. 25 ( 1987) 576-582. | Zbl | MR
[11] and , Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Engrg. 2 ( 1973) 17-31. | Zbl | MR
[12] , Elliptic Differential Equations, Theory and Numerical Treatment. Springer Verlag, Berlin, Ser. Comput. Math. 18 ( 1992). | Zbl | MR
[13] and , An augmented Lagrangian technics for variational inequalities. Appl. Math. Optim. 21 ( 1990) 223-241. | Zbl | MR
[14] and , Optimal control of elliptic variational inequalities, to appear. | Zbl | MR
[15] , On the existence and nonexistence of Lagrange multipliers in Banach spaces. J. Optim. Theory Appl. 5 ( 1976). 81-110. | Zbl | MR
[16] , Contrôle dans les inéquations variationnelles elliptiques. J. Funct. Anal. 22 ( 1976) 130-185. | Zbl | MR
[17] and , Optimal control in some variational inequalities. SIAM J. Control Optim. 22 ( 1984) 466-476. | Zbl | MR
[18] and , Contrôle optimal d'un système gouverné par une inéquation variationnelle parabolique. C. R. Acad. Sci. Paris Sér. I Math. 298 ( 1984) 277-280. | Zbl | MR
[19] and , Error estimates for the discretization of state constrained convex control problems. Num. Funct. Anal. Optim. 17 ( 1996) 1005-1028. | Zbl | MR
[20] and , Optimality conditions for strongly monotone variational inequalities. Appl. Math. Optim. 27 ( 1993) 291-312. | Zbl | MR
[21] and , Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 ( 1979) 49-62. | Zbl | MR






