A regularization method for the numerical solution of elliptic boundary control problems with pointwise state constraints

Computational Optimization and Applications

Volumn 42, Issue 1, 2009, Pages 43-66

  Troltzsch F ^a   Yousept, I ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Boundary control; Lavrentiev type regularization; Nested iteration; Optimize then discretize; Semismooth Newton method; State constraints

Indexed keywords

BOUNDARY CONTROL; LAVRENTIEV TYPE REGULARIZATION; NESTED ITERATION; OPTIMIZE-THEN-DISCRETIZE; SEMISMOOTH NEWTON METHOD; STATE CONSTRAINTS;

NEWTON-RAPHSON METHOD;

EID: 58149497486     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9114-0     Document Type: Article

References (15)

1. J.-J. Alibert J.-P. Raymond 1997 Boundary control of semilinear elliptic equations with discontinuous leading coefficients and unbounded controls Numer. Funct. Anal. Optim. 3&4 235 250
2. M. Bergounioux K. Ito K. Kunisch 1999 Primal-dual strategy for constrained optimal control problems SIAM J. Control Optim. 37 1176 1194
3. M. Bergounioux K. Kunisch 2002 Primal-dual active set strategy for state-constrained optimal control problems Comput. Optim. Appl. 22 193 224
4. E. Casas 1986 Control of an elliptic problem with pointwise state constraints SIAM J. Control Optim. 4 1309 1322
5. E. Casas 1993 Boundary control of semilinear elliptic equations with pointwise state constraints SIAM J. Control Optim. 31 993 1006
6. X. Chen Z. Nashed L. Qi 2000 Smoothing methods and semismooth methods for nondifferentiable operator equations SIAM J. Numer. Anal. 38 4 1200 1216 (electronic)
7. Hackbusch, W.: Multigrid Methods and Applications. Springer Series in Computational Mathematics, vol. 4. Springer, Berlin (1985)
8. M. Hintermüller K. Ito K. Kunisch 2003 The primal-dual active set strategy as a semismooth Newton method SIAM J. Optim. 13 865 888
9. Hintermüller, M., Tröltzsch, F., Yousept, I.: Mesh-independence of semismooth Newton methods for Lavrentiev-regularized state constrained nonlinear optimal control problems (2006)
10. K. Ito K. Kunisch 2000 Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces Nonlinear Anal. TMA 41 591 616
11. K. Ito K. Kunisch 2003 Semi-smooth Newton methods for state-constrained optimal control problems Syst. Control Lett. 50 221 228
12. Lavrentiev, M.M.: Some Improperly Posed Problems of Mathematical Physics. Springer, New York (1967)
13. H. Maurer H.D. Mittelmann 2000 Optimization techniques for solving elliptic control problems with control and state constraints. I. Boundary control J. Comput. Appl. Math. 16 29 55
14. C. Meyer A. Rösch F. Tröltzsch 2006 Optimal control of PDEs with regularized pointwise state constraints Comput. Optim. Appl. 33 209 228
15. Meyer, C., Tröltzsch, F.: On an elliptic optimal control problem with pointwise mixed control-state constraints. In: Seeger, A. (ed.) Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization held in Avignon, September 20-24, 2004. Lectures Notes in Economics and Mathematical Systems, vol. 563, pp. 187-204. Springer, Berlin (2006)