EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 / No 3 (July-September 2011) ESAIM: COCV, 17 3 (2011) 858-886 References
Free Access
Issue
ESAIM: COCV
Volume 17, Number 3, July-September 2011
Page(s) 858 - 886
DOI https://doi.org/10.1051/cocv/2010027
Published online 06 August 2010
  1. N. Aronszajn, Differentiability of Lipschitzian mappings between Banach spaces. Studia Math. 57 (1976) 147–190. [MathSciNet] [Google Scholar]
  2. R. Becker and R. Rannacher, An optimal control approach to a posteriori error estimation in finite element methods. Acta Numer. 10 (2001) 1–102. [CrossRef] [MathSciNet] [Google Scholar]
  3. C. Carstensen, Quasi-interpolation and a posteriori error analysis in finite element methods. ESAIM: M2AN 33 (1999) 1187–1202. [CrossRef] [EDP Sciences] [Google Scholar]
  4. E. Casas and M. Mateos, Error estimates for the numerical approximation of boundary semilinear elliptic control problems. Continuous piecewise linear approximations, in Systems, control, modeling and optimization 202, IFIP Int. Fed. Inf. Process., Springer, New York (2006) 91–101. [Google Scholar]
  5. C. Clason and K. Kunisch, A duality-based approach to elliptic control problems in non-reflexive Banach spaces. ESAIM: COCV (2010) DOI: 10.1051/cocv/2010003. [Google Scholar]
  6. I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. Pure Appl. Math. 57 (2004) 1413–1457. [Google Scholar]
  7. D. Donoho, For most large underdetermined systems of linear equations the minimal l1-norm solution is also the sparsest solution. Comm. Pure Appl. Math. 59 (2006) 797–829. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.L. Dontchev, W.W. Hager, A.B. Poore and B. Yang, Optimality, stability and convergence in optimal control. Appl. Math. Optim. 31 (1995) 297–326. [CrossRef] [MathSciNet] [Google Scholar]
  9. R.S. Falk, Approximation of a class of optimal control problems with order of convergence estimates. J. Math. Anal. Appl. 44 (1973) 28–47. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Grasmair, M. Haltmeier and O. Scherzer, Sparse regularization with lq penalty term. Inv. Prob. 24 (2008) 055020. [Google Scholar]
  11. R. Griesse and D.A. Lorenz, A semismooth Newton method for Tikhonov functionals with sparsity constraints. Inv. Prob. 24 (2008) 035007. [Google Scholar]
  12. R. Griesse, T. Grund and D. Wachsmuth, Update strategies for perturbed nonsmooth equations. Optim. Methods Softw. 23 (2008) 321–343. [Google Scholar]
  13. M. Hintermüller, R.H.W. Hoppe, Y. Iliash and M. Kieweg, An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints. ESAIM: COCV 14 (2008) 540–560. [CrossRef] [EDP Sciences] [Google Scholar]
  14. M. Hinze, A variational discretization concept in control constrained optimization: the linear-quadratic case. Comp. Optim. Appl. 30 (2005) 45–63. [CrossRef] [Google Scholar]
  15. A.D. Ioffe and V.M. Tichomirov, Theorie der Extremalaufgaben. VEB Deutscher Verlag der Wissenschaften, Berlin (1979). [Google Scholar]
  16. B. Jin, D.A. Lorenz and S. Schiffler, Elastic-net regularization: error estimates and active set methods. Inv. Prob. 25 (2009) 115022. [CrossRef] [Google Scholar]
  17. K. Krumbiegel and A. Rösch, A new stopping criterion for iterative solvers for control constrained optimal control problems. Archives of Control Sciences 18 (2008) 17–42. [MathSciNet] [Google Scholar]
  18. R. Li, W. Liu, H. Ma and T. Tang, Adaptive finite element approximation for distributed elliptic optimal control problems. SIAM J. Control Optim. 41 (2002) 1321–1349. [CrossRef] [MathSciNet] [Google Scholar]
  19. R. Li, W. Liu and N. Yan, A posteriori error estimates of recovery type for distributed convex optimal control problems. J. Sci. Comput. 33 (2007) 155–182. [CrossRef] [MathSciNet] [Google Scholar]
  20. W. Liu and N. Yan, A posteriori error estimates for convex boundary control problems. SIAM J. Numer. Anal. 39 (2001) 73–99. [CrossRef] [MathSciNet] [Google Scholar]
  21. D.A. Lorenz, Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inverse Ill-Posed Probl. 16 (2008) 463–478. [Google Scholar]
  22. D.A. Lorenz and A. Rösch, Error estimates for joint Tikhonov- and Lavrentiev-regularization of constrained control problems. Appl. Anal. (to appear). [Google Scholar]
  23. C. Meyer and A. Rösch, Superconvergence properties of optimal control problems. SIAM J. Control Optim. 43 (2004) 970–985. [CrossRef] [MathSciNet] [Google Scholar]
  24. C. Meyer, J.C. de los Reyes and B. Vexler, Finite element error analysis for state-constrained optimal control of the Stokes equations. Control Cybern. 37 (2008) 251–284. [Google Scholar]
  25. R. Ramlau and G. Teschke, A Tikhonov-based projection iteration for nonlinear ill-posed problems with sparsity constraints. Numer. Math. 104 (2006) 177–203. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Schiela, Barrier methods for optimal control problems with state constraints. SIAM J. Optim. 20 (2009) 1002–1031. [CrossRef] [MathSciNet] [Google Scholar]
  27. G. Stadler, Elliptic optimal control problems with L1-control cost and applications for the placement of control devices. Comp. Optim. Appl. 44 (2009) 159–181. [Google Scholar]
  28. G. Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15 (1965) 189–258. [CrossRef] [MathSciNet] [Google Scholar]
  29. F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Vieweg, Wiesbaden (2005). [Google Scholar]
  30. G. Wachsmuth, Elliptische Optimalsteuerungsprobleme unter Sparsity-Constraints. Diploma Thesis, Technische Universität Chemnitz (2008) http://www.tu-chemnitz.de/mathematik/part_dgl/publications.php+. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.