Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 79
Number of page(s) 30
DOI https://doi.org/10.1051/cocv/2022075
Published online 23 December 2022
  1. W. Alt, C. Schneider and M. Seydenschwanz, Regularization and implicit Euler discretization of linear-quadratic optimal control problems with bang-bang solutions. Appi. Math. Comput. 287/288 (2016) 104-124. [CrossRef] [Google Scholar]
  2. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer Series in Operations Research. SpringerVerlag, New York (2000). [Google Scholar]
  3. R.S. Burachik and V. Jeyakumar, A simple closure condition for the normal cone intersection formula. Proc. Am. Math. Soc. 133 (2005) 1741-1748. [Google Scholar]
  4. E. Casas, Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J. Control Optim. 31 (1993) 993-1006. [Google Scholar]
  5. E. Casas, Second order analysis for bang-bang control problems of PDEs. SIAM J. Control Optim. 50 (2012) 2355-2372. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Casas and K. Chrysafìnos, Error estimates for the approximation of the velocity tracking problem with bang-bang controls. ESAIM: COCV 23 (2017) 1267-1291. [CrossRef] [EDP Sciences] [Google Scholar]
  7. E. Casas, J.C. de los Reyes and F. Tröltzsch, Sufficient second-order optimality conditions for semilinear control problems with pointwise state constraints. SIAM J. Optim. 19 (2008) 616-643. [Google Scholar]
  8. E. Casas, M. Mateos and A. Rösch, Analysis of control problems of nonmontone semilinear elliptic equations. ESAIM: COCV 26 (2020) Paper No. 80, 21. [CrossRef] [EDP Sciences] [Google Scholar]
  9. E. Casas and F. Tröltzsch, On optimal control problems with controls appearing nonlinearly in an elliptic state equation. SIAM J. Control Optim. 58 (2020) 1961-1983. [CrossRef] [MathSciNet] [Google Scholar]
  10. E. Casas, D. Wachsmuth and G. Wachsmuth, Sufficient second-order conditions for bang-bang control problems. SIAM J. Control Optim. 55 (2017) 3066-3090. [CrossRef] [MathSciNet] [Google Scholar]
  11. E. Casas, D. Wachsmuth and G. Wachsmuth, Second-order analysis and numerical approximation for bang-bang bilinear control problems. SIAM J. Control Optim. 56 (2018) 4203-4227. [Google Scholar]
  12. R. Cibulka, A.L. Dontchev and A.Y. Kruger, Strong metric subregularity of mappings in variational analysis and optimization. J. Math. Anal. Appl. 457 (2018) 1247-1282. [Google Scholar]
  13. K. Deckelnick and M. Hinze, A note on the approximation of elliptic control problems with bang-bang controls. Comput. Optim. Appl. 51 (2012) 931-939. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Dominguez Corella, M. Quincampoix and V.M. Veliov, Strong bi-metric regularity in affine optimal control problems. Pure Appl. Funct. Anal. 6 (2021) 1119-1137. [MathSciNet] [Google Scholar]
  15. A. Dominguez Corella and V.M. Veliov, Hölder regularity in bang-bang type affine optimal control problems, in Large-scale scientific computing, volume 13127 of Lecture Notes in Comput. Sci.. Springer, Cham (2022), pp. 306-313. [CrossRef] [Google Scholar]
  16. A.L. Dontchev, I.V. Kolmanovsky, M.I. Krastanov, V.M. Veliov and P.T. Vuong, Approximating optimal finite horizon feedback by model predictive control. Syst. Control Lett. 139 (2020) 104666. [Google Scholar]
  17. A.L. Dontchev and R.T. Rockafellar, Implicit functions and solution mappings. Springer Monographs in Mathematics. Springer, Dordrecht (2009) A view from variational analysis. [Google Scholar]
  18. W.H. Fleming and R.W. Rishel, Deterministic and Stochastic Optimal Control. Springer-Verlag, Berlin-New York (1975). [Google Scholar]
  19. R. Griesse, Lipschitz stability of solutions to some state-constrained elliptic optimal control problems. Z. Anal. Anwend. 25 (2006) 435-455. [CrossRef] [MathSciNet] [Google Scholar]
  20. P. Grisvard, Elliptic problems in nonsmooth domains, volume 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  21. R. Haller-Dintelmann, C. Meyer, J. Rehberg and A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems. Appl. Math. Optim. 60 (2009) 397-428. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Hinze and C. Meyer, Stability of semilinear elliptic optimal control problems with pointwise state constraints. Comput. Optim. Appl. 52 (2012) 87-114. [CrossRef] [MathSciNet] [Google Scholar]
  23. B.T. Kien, N.Q. Tuan, C.-F. Wen and J.-C. Yao. L1-stability of a parametric optimal control problem governed by semilinear elliptic equations. Appl. Math. Optim. 84 (2021) 849-876. [CrossRef] [MathSciNet] [Google Scholar]
  24. D. Luenberger, Optimization by Vector Space Methods. Wiley-Interscience (1969). [Google Scholar]
  25. K. Malanowski and F. Tröoltzsch, Lipschitz stability of solutions to parametric optimal control for elliptic equations. Control Cybernet. 29 (2000) 237-256. [MathSciNet] [Google Scholar]
  26. B.S. Mordukhovich and T.T.A. Nghia, Full Lipschitzian and Höolderian stability in optimization with applications to mathematical programming and optimal control. SIAM J. Optim. 24 (2014) 1344-1381. [CrossRef] [MathSciNet] [Google Scholar]
  27. J.R. Munkres, Topology: a first course, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1975). [Google Scholar]
  28. R. Nittka, Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains. J. Differ. Equ. 251 (2011) 860-880. [Google Scholar]
  29. N.P. Osmolovskii and V.M. Veliov, Metric sub-regularity in optimal control of affine problems with free end state. ESAIM: COCV 26 (2020) Paper No. 47, 19. [CrossRef] [EDP Sciences] [Google Scholar]
  30. N.P. Osmolovskii and V.M. Veliov, On the regularity of Mayer-type affine optimal control problems, In Large-scale scientific computing, volume 11958 of Lecture Notes in Comput. Sci.. Springer, Cham (2020), pp. 56-63. [Google Scholar]
  31. F. Pöorner and D. Wachsmuth, An iterative Bregman regularization method for optimal control problems with inequality constraints. Optimization 65 (2016) 2195-2215. [CrossRef] [MathSciNet] [Google Scholar]
  32. F. Pöorner and D. Wachsmuth, Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations. Math. Control Relat. Fields 8 (2018) 315-335. [CrossRef] [MathSciNet] [Google Scholar]
  33. F. Pöorner and D. Wachsmuth, Tikhonov regularization of optimal control problems governed by semi-linear partial differential equations. Math. Control Relat. Fields 8 (2018) 315-335. [CrossRef] [MathSciNet] [Google Scholar]
  34. J. Preininger, T. Scarinci and V.M. Veliov, On the regularity of linear-quadratic optimal control problems with bang-bang solutions, In Large-scale scientific computing, volume 10665 of Lecture Notes in Comput. Sci.. Springer, Cham (2018), pp. 237-245. [Google Scholar]
  35. N.T. Qui and D. Wachsmuth, Stability for bang-bang control problems of partial differential equations. Optimization 67 (2018) 2157-2177. [CrossRef] [MathSciNet] [Google Scholar]
  36. N.T. Qui and D. Wachsmuth, Full stability for a class of control problems of semilinear elliptic partial differential equations. SIAM J. Control Optim. 57 (2019) 3021-3045. [CrossRef] [MathSciNet] [Google Scholar]
  37. S.M. Robinson, Generalized equations and their solutions. I. Basic theory. Math. Programming Stud., (10) (1979) 128-141. Point-to-set maps and mathematical programming. [CrossRef] [Google Scholar]
  38. M. Seydenschwanz, Convergence results for the discrete regularization of linear-quadratic control problems with bang-bang solutions. Comput. Optim. Appl. 61 (2015) 731-760. [Google Scholar]
  39. 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]
  40. F. Tröltzsch, Optimal control of partial differential equations, volume 112 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2010). Theory, methods and applications, Translated from the 2005 German original by JUrgen Sprekels. [CrossRef] [Google Scholar]
  41. A. Visintin, Strong convergence results related to strict convexity. Comm. Partial Differ. Equ. 9 (1984) 439-466. [CrossRef] [Google Scholar]
  42. N. von Daniels, Tikhonov regularization of control-constrained optimal control problems. Comput. Optim. Appl. 70 (2018) 295-320. [CrossRef] [MathSciNet] [Google Scholar]
  43. D. Wachsmuth and G. Wachsmuth, Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints. Control Cybernet. 40 (2011) 1125-1158. [MathSciNet] [Google Scholar]
  44. G. Wachsmuth and D. Wachsmuth, Convergence and regularization results for optimal control problems with sparsity functional. ESAIM: COCV 17 (2011) 858-886. [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.