Issue
ESAIM: COCV
Volume 27, 2021
Special issue in honor of Enrique Zuazua's 60th birthday
Article Number 4
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2020059
Published online 20 January 2021
  1. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford University Press, Oxford & New York (2000). [Google Scholar]
  2. M.S. Aronna, J.F. Bonnans and A. Kröner, State-constrained control-affine parabolic problems I: first and second order necessary optimality conditions. Preprint arXiv:1906.00237 (2019). [Google Scholar]
  3. H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces. SIAM, Philadelphia (2006). [Google Scholar]
  4. V. Barbu, Optimal Control of Variational Inequalities. Research Notes in Mathematics. Pitman (1984). [Google Scholar]
  5. M. Bergounioux, Optimal control of parabolic problems with state constraints: a penalization method for optimality conditions. Appl. Math. Optim. 29 (1994) 285–307. [Google Scholar]
  6. M. Bergounioux and K. Kunisch, Primal-dual strategy for state-constrained optimal control problems. Comput. Optim. Appl. 22 (2002) 193–224. [Google Scholar]
  7. L. Bonifacius, Numerical Analysis of Parabolic Time-optimal Control Problems. Ph.D. thesis, Technische Universität München (2018). [Google Scholar]
  8. J. Bonnans and P. Jaisson, Optimal control of a parabolic equation with time-dependent state constraints. SIAM J. Control Optim. 48 (2010) 4550–4571. [Google Scholar]
  9. J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer, New York (2000). [Google Scholar]
  10. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods, 3rd edn. Springer (2008). [Google Scholar]
  11. E. Casas, Pontryagin’s principle for state-constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 (1997) 1297–1327. [Google Scholar]
  12. E. Casas, M. Mateos and B. Vexler, New regularity results and improved error estimates for optimal control problems with state constraints. ESAIM: COCV 20 (2014) 803–822. [Google Scholar]
  13. E. Casas and F. Tröltzsch, Recent advances in the analysis of pointwise state-constrained elliptic optimal control problems. ESAIM Control Optim. Calc. Var. 16 (2010) 581–600. [Google Scholar]
  14. C. Christof, Sensitivity Analysis of Elliptic Variational Inequalities of the First and the Second Kind. Ph.D. thesis, Technische Universität Dortmund (2018). [Google Scholar]
  15. C. Christof, Sensitivity analysis and optimal control of obstacle-type evolution variational inequalities. SIAM J. Control Optim. 57 (2019) 192–218. [Google Scholar]
  16. C. Christof and C. Meyer, A note on a priori Lp-error estimatesfor the obstacle problem. Numer. Math. 139 (2018) 27–45. [Google Scholar]
  17. C. Christof and C. Meyer. Sensitivity analysis for a class of H01-elliptic variational inequalities of the second kind. Set-Valued Var. Anal. 27 (2018) 469–502. [Google Scholar]
  18. C. Christof and G. Wachsmuth, On second-order optimality conditions for optimal control problems governed by the obstacle problem. To appear in: Optimization (2020) 1–41. https://doi.org/10.1080/02331934.2020.1778686. [Google Scholar]
  19. F.H. Clarke, Optimization and Nonsmooth Analysis. SIAM’s Classics in Applied Mathematics. SIAM, Philadelphia, PA (1990). [Google Scholar]
  20. J.C. De Los Reyes, P. Merino, J. Rehberg and F. Tröltzsch, Optimality conditions for state-constrained PDE control problems with time-dependent controls. Control Cybernet. 37 (2008) 5–38. [Google Scholar]
  21. J.C. De Los Reyes and C. Meyer, Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the second kind. J. Optim. Theory Appl. 168 (2016) 375–409. [Google Scholar]
  22. K. Deckelnick and M. Hinze, Variational discretization of parabolic control problems in the presence of pointwise state constraints. J. Comput. Math. 29 (2011) 1–15. [Google Scholar]
  23. K. Disser, A.F.M. ter Elst and J. Rehberg, Hölder estimates for parabolic operators on domains with rough boundary. Ann. Sc. Norm. Super. Pisa Cl. Sci. XVII (2017) 65–79. [Google Scholar]
  24. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland (1976). [Google Scholar]
  25. J. Elschner, J. Rehberg and G. Schmidt, Optimal regularity for elliptic transmission problems including C1 -interfaces. Interfaces Free Bound. 9 (2007) 233–252. [Google Scholar]
  26. K. Eriksson, C. Johnson and V. Thomée, Time discretization of parabolic problems by the discontinuous Galerkin method. ESAIM Math. Model. Numer. Anal. 19 (1985) 611–643. [Google Scholar]
  27. L.C. Evans, Partial Differential Equations, 2nd edn. AMS, Providence, RI (2010). [Google Scholar]
  28. L.A. Fernández, State Constrained Optimal Control for Some Quasilinear Parabolic Equations, edited by K.-H. Hoffmann, G. Leugering, F. Tröltzsch and S. Caesar. Optimal Control of Partial Differential Equations. Birkhäuser, Basel, (1999) 145–156. [Google Scholar]
  29. L.A. Fernández, Integral state-constrained optimal control problems for some quasilinear parabolic equations. J. Nonlinear Anal. Optim. 39 (2000) 977–996. [Google Scholar]
  30. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, reprint ofthe 1998 edn. Springer 2001. [Google Scholar]
  31. R. Glowinski, Y. Song and X. Yuan, An ADMM numerical approach to linear parabolic state constrained optimal control problems. Numer. Math. 144 (2020) 931–966. [Google Scholar]
  32. W. Gong and M. Hinze, Error estimates for parabolic optimal control problems with control and state constraints. Comput. Optim. Appl. 56 (2013) 131–151. [Google Scholar]
  33. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman (1985). [Google Scholar]
  34. F. Harder and G. Wachsmuth. Comparison of optimality systems for the optimal control of the obstacle problem. GAMM-Mitt. 40 (2018) 312–338. [Google Scholar]
  35. J. Heinonen, P. Koselka, N. Shanmugalingam and J.T. Tyson, Sobolev Spaces on Metric Measure Spaces. Vol. 27 of New Mathematical Monographs. Cambridge University Press (2015). [Google Scholar]
  36. M. Hinze. A variational discretization concept in control constrained optimization: the linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [Google Scholar]
  37. K. Ito and K. Kunisch, Semi-smooth Newton methods for state-constrained optimal control problems. Systems Control Lett. 50 (2003) 221–228. [Google Scholar]
  38. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Vol. 31 of Classics in Applied Mathematics. SIAM (2000). [Google Scholar]
  39. D. Leykekhman and B. Vexler, Pointwise best approximation results for Galerkin finite element solutions of parabolic problems. SIAM J. Numer. Anal. 54 (2016) 1365–1384. [Google Scholar]
  40. D. Leykekhman and B. Vexler, Discrete maximal parabolic regularity for Galerkin finite element methods. Numer. Math. 135 (2017) 923–952. [Google Scholar]
  41. F. Ludovici, I. Neitzel and W. Wollner, A priori error estimates for state-constrained semilinear parabolic optimal control problems. J. Optim. Theory Appl. 178 (2018) 317–348. [Google Scholar]
  42. D. Meidner, R. Rannacher and B. Vexler, A priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time. SIAM J. Control Optim. 49 (2011) 1961–1997. [Google Scholar]
  43. D. Meidner and B. Vexler, Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations. ESAIM: M2AN 52 (2018) 2307–2325. [Google Scholar]
  44. C. Meyer, A. Rösch and F. Tröltzsch, Optimal control of PDEs with regularized pointwise state constraints. Comput. Optim. Appl. 33 (2006) 209–228. [Google Scholar]
  45. F. Mignot, Contrôle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [Google Scholar]
  46. B.S. Mordukhovich and K. Zhang, Optimal control of state-constrained parabolic systems with nonregular boundary controllers, in Proceedings of the 36th IEEE Conference on Decision and Control, Vol. 1 (1997) 527–528. [Google Scholar]
  47. J.J. Moreau, P.D. Panagiotopoulos and G. Strang, Topics in Nonsmooth Mechanics. Birkhäuser, Basel (1988). [Google Scholar]
  48. I. Neitzel and F. Tröltzsch, On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints. Control Cybernet. 37 (2008) 1013–1043. [Google Scholar]
  49. I. Neitzel and F. Tröltzsch, On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints. ESAIM: COCV 15 (2009) 426–453. [Google Scholar]
  50. I. Neitzel and F. Tröltzsch, Numerical analysis of state-constrained optimal control problems for PDEs, edited by G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich and S. Ulbrich Constrained Optimization and Optimal Control for Partial Differential Equations. Springer, Basel (2012) 467–482. [CrossRef] [Google Scholar]
  51. A.H. Schatz and L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, part II. Math. Comput. 64 (1995) 907–928. [Google Scholar]
  52. A. Schiela, State constrained optimal control problems with states of low regularity. SIAM J. Control Optim. 48 (2009) 2407–2432. [Google Scholar]
  53. B. Schweizer, Partielle Differentialgleichungen. Springer, Berlin/Heidelberg (2013). [CrossRef] [Google Scholar]
  54. F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen. Vieweg und Teubner, Wiesbaden, 2nd edn. (2009). [CrossRef] [Google Scholar]
  55. D. Wachsmuth, The regularity of the positive part of functions in L2 (I ; H1 (Ω)) ∩ H1 (I ; H1 (Ω) *) with applications to parabolic equations. Comment. Math. Univ. Carolin. 57 (2016) 327–332. [Google Scholar]
  56. G. Wachsmuth, Towards M-stationarity for optimal control of the obstacle problem with control constraints. SIAM J. Control Optim. 54 (2016) 964–986. [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.