Optimal control of obstacle problems: Existence of lagrange multipliers

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 5, Issue , 2000, Pages 45-70

  Bergounioux, Maïtine ^a   Mignot, Fulbert ^b  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Lagrange multiplier; Obstacle problem; Optimal control; Variational inequalities

Indexed keywords

CONTROL SYSTEM ANALYSIS; DIFFERENTIATION (CALCULUS); LAGRANGE MULTIPLIERS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

MOREAU-YOSIDA TYPE; OBSTACLE PROBLEMS; POINTWISE CONSTRAINT; VARIATIONAL INEQUALITY;

OPTIMAL CONTROL SYSTEMS;

EID: 0034426076     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2000101     Document Type: Article

References (21)

1. D.R. Adams, S. Lenhart and J. Yong, Optimal control of variational inequalities. Appl. Math. Optim. 38 (1998) 121-140.
2. V. Barbu, Optimal control of variational inequalities. Pitman, Boston, Res. Notes Math. 100 (1984).
3. M. Bergounioux, Optimal control of an obstacle problem. Appl. Math. Optim. 36 (1997) 147-172.
4. M. Bergounioux, Optimal control of problems governed by abstract variational inequalities with state constraints. SIAM J. Control Optim. 36 (1998) 273-289.
5. M. Bergounioux, Augmented lagrangian method for distributed optimal control problems with state constraints. J. Optim. Theory Appl. 78 (1993) 493-521.
6. M. Bergounioux and H. Dietrich, Optimal control of problems governed by obstacle type variational inequalities: A dual regularization-penalization approach. J. Convex Anal. 5 (1998) 329-351.
7. M. Bergounioux, M. Haddou, M. Hintermueller and K. Kunisch, A comparison of interior point methods and a Moreau-Yosida based active set strategy for constrained optimal control problems. Report 98-15 Universite d’Orleans (1998).
8. M. Bergounioux and H. Zidani, Pontryagin principle for problems governed by parabolic variational inequalities. SIAM J. Control Optim. 37 (1999) 1273-1290.
9. A. Bermudez and C. Saguez, 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.
10. A. Bermudez and C. Saguez, Optimal control of a Signorini Problem. SIAM J. Control Optim. 25 (1987) 576-582.
11. P.G. Ciarlet and P.A. Raviart, Maximum principle and uniform convergence for the finite element method. Comput. Methods Appl. Mech. Engrg. 2 (1973) 17-31.
12. W. Hackbusch, Elliptic Differential Equations, Theory and Numerical Treatment. Springer Verlag, Berlin, Ser. Comput. Math. 18 (1992).
13. K. Ito and K. Kunisch, An augmented Lagrangian technics for variational inequalities. Appl. Math. Optim. 21 (1990) 223-241.
14. K. Ito and K. Kunisch, Optimal control of elliptic variational inequalities, to appear.
15. S. Kurcyusz, On the existence and nonexistence of Lagrange multipliers in Banach spaces. J. Optim. Theory Appl. 5 (1976) 81-110.
16. F. Mignot, Contrôle dans les inéquations variationnelles elliptiques. J. Funct. Anal. 22 (1976) 130-185.
17. F. Mignot and J.P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466-476.
18. F. Mignot and J.P. Puel, Côntrole optimal d’un système gouverné par une inéquation variationnelle parabolique. C. R. Acad. Sci. Paris Sér. I Math. 298 (1984) 277-280.
19. D. Tiba and F. Tröltzsch, Error estimates for the discretization of state constrained convex control problems. Num. Funct. Anal. Optim. 17 (1996) 1005-1028.
20. L. Wenbin and J.E. Rubio, Optimality conditions for strongly monotone variational inequalities. Appl. Math. Optim. 27 (1993) 291-312.
21. J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 (1979) 49-62.