EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 60 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 60
Number of page(s) 25
DOI https://doi.org/10.1051/cocv/2024048
Published online 28 August 2024
  1. A. Domínguez Corella and V.M. Veliov, Hölder regularity in bang-bang type affine optimal control problems, in Large-scale Scientific Computing. Vol. 13127 of Lecture Notes in Comput. Sci., Springer, Cham (2022) 306–313. [CrossRef] [Google Scholar]
  2. U. Felgenhauer, On stability of bang-bang type controls. SIAM J. Control Optim. 41 (2003) 1843–1867. [CrossRef] [MathSciNet] [Google Scholar]
  3. H. Maurer and N.P. Osmolovskii, Second order sufficient conditions for time-optimal bang-bang control. SIAM J. Control Optim. 42 (2004) 2239–2263. [CrossRef] [MathSciNet] [Google Scholar]
  4. A.A. Milyutin and N.P. Osmolovskii, Calculus of Variations and Optimal Control. Vol. 180 of Translations of Mathematical Monographs. American Mathematical Society, Providence, RI (1998). [CrossRef] [Google Scholar]
  5. N.P. Osmolovskii and H. Maurer, Equivalence of second order optimality conditions for bang-bang control problems. I. Main results. Control Cybernet. 34 (2005) 927–950. [MathSciNet] [Google Scholar]
  6. N.P. Osmolovskii and H. Maurer, Equivalence of second order optimality conditions for bang-bang control problems. II. Proofs, variational derivatives and representations. Control Cybernet. 36 (2007) 5–45. [MathSciNet] [Google Scholar]
  7. N.P. Osmolovskii and V.M. Veliov, On the regularity of Mayer-type affine optimal control problems, in Large-scale Scientific Computing. Vol. 11958 of Lecture Notes in Comput. Sci. Springer (2020) 56–63. [CrossRef] [Google Scholar]
  8. 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. Vol. 10665 of Lecture Notes in Comput. Sci.. Springer, Cham (2018) 237–245. [CrossRef] [Google Scholar]
  9. J. Preininger, T. Scarinci and V.M. Veliov, Metric regularity properties in bang-bang type linear-quadratic optimal control problems. Set-Valued Var. Anal. 27 (2019) 381–404. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Quincampoix and V.M. Veliov, Metric regularity and stability of optimal control problems for linear systems. SIAM J. Control Optim. 51 (2013) 4118–4137. [CrossRef] [MathSciNet] [Google Scholar]
  11. E. Casas, Second order analysis for bang-bang control problems of PDEs. SIAM J. Control Optim. 50 (2012) 2355–2372. [Google Scholar]
  12. J.F. Bonnans, Optimal control of a semilinear parabolic equation with singular arcs. Optim. Methods Softw. 29 (2014) 964–978. [CrossRef] [MathSciNet] [Google Scholar]
  13. E. Casas, M. Mateos and A. Rösch, Error estimates for semilinear parabolic control problems in the absence of Tikhonov term. SIAM J. Control Optim. 57 (2019) 2515–2540. [CrossRef] [MathSciNet] [Google Scholar]
  14. E. Casas, C. Ryll and F. Tröltzsch, Second order and stability analysis for optimal sparse control of the FitzHugh- Nagumo equation. SIAM J. Control Optim. 53 (2015) 2168–2202. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Casas and F. Tröltzsch, Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls. SIAM J. Control Optim. 52 (2014) 1010–1033. [CrossRef] [MathSciNet] [Google Scholar]
  16. E. Casas and F. Tröltzsch, Second-order optimality conditions for weak and strong local solutions of parabolic optimal control problems. Vietnam J. Math. 44 (2016) 181–202. [CrossRef] [MathSciNet] [Google Scholar]
  17. E. Casas, D. Wachsmuth and G. Wachsmuth, Sufficient second-order conditions for bang-bang control problems. SIAM J. Control Optim. 55 (2017) 3066–3090. [Google Scholar]
  18. E. Casas, A. Domínguez Corella and N. Jork, New assumptions for stability analysis in elliptic optimal control problems. SIAM J. Control Optim. 61 (2023) 1394–1414. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Domínguez Corella, N. Jork and V. Veliov, Stability in affine optimal control problems constrained by semilinear elliptic partial differential equations. ESAIM Control Optim. Calc. Var. 28 (2022) Paper No. 79. [Google Scholar]
  20. A. Domínguez Corella, N. Jork and V. Veliov, On the solution stability of parabolic optimal control problems. Comput. Optim. Appl. 86 (2023) 1035–1079. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. E. Casas and M. Mateos, State error estimates for the numerical approximation of sparse distributed control problems in the absence of Tikhonov regularization. Vietnam J. Math. 49 (2021) 713–738. [CrossRef] [MathSciNet] [Google Scholar]
  22. 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. [CrossRef] [MathSciNet] [Google Scholar]
  23. K. Deckelnick and M. Hinze, 1. Comput. Optim. Appl. 51 (2012) 931–939. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Casas and M. Mateos, Critical cones for sufficient second-order conditions in PDE constrained optimization. SIAM J. Optim. 30 (2020) 585–603. [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Mazari, Quantitative inequality for the eigenvalue of a Schroodinger operator in the ball. J. Diff. Equ. 269 (2020) 10181–10238. [CrossRef] [Google Scholar]
  26. I. Mazari, Quantitative estimates for parabolic optimal control problems under L∞ and L1 constraints in the ball: quantifying parabolic isoperimetric inequalities. Nonlinear Anal. 215 (2022) Paper No. 112649. [CrossRef] [Google Scholar]
  27. E. Casas, M. Mateos and A. Rösch, Analysis of control problems of nonmontone semilinear elliptic equations. ESAIM Control Optim. Calc. Var. 26 (2020) Paper No. 80. [CrossRef] [EDP Sciences] [Google Scholar]
  28. E. Casas, M. Mateos and A. Rösch, Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations. Numer. Math. 149 (2021) 305–340. [CrossRef] [MathSciNet] [Google Scholar]
  29. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Vol. 224 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn. Springer-Verlag, Berlin (1983). [Google Scholar]
  30. 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]
  31. F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications. Vol. 112 of Graduate Studies in Mathematics. American Mathematical Society, Philadelphia (2010). [CrossRef] [Google Scholar]
  32. T. Bayen, J.F. Bonnans and F.J. Silva, Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations. Trans. Amer. Math. Soc. 366 (2014) 2063–2087. [Google Scholar]
  33. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  34. E. Casas, Pontryagin’s principle for optimal control problems governed by semilinear elliptic equations, in Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena (Vorau, 1993). Vol. 118 of Internat. Ser. Numer. Math. Birkhäuser, Basel (1994) 97–114. [CrossRef] [Google Scholar]
  35. S.C. Brenner and L.R. Scott, The Mathematical Theory of Finite Element Methods. Vol. 15 of Texts in Applied Mathematics, 2nd edn. Springer-Verlag, New York (2002). [CrossRef] [Google Scholar]
  36. P.A. Raviart and J.M. Thomas, Introduction à l’analyse numérique des équations aux dérivées partielles. (1983). [Google Scholar]
  37. E. Casas and M. Mateos, Uniform Convergence of the FEM. Applications to State Constrained Control Problems. Vol. 21 (2002) 67–100. [Google Scholar]
  38. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992). [Google Scholar]
  39. J. Bourgain, J. Kristensen and M.V. Korobkov, On the Morse-Sard property and level sets of Sobolev and BV functions. Rev. Mat. Iberoam. 29 (2013) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  40. L. De Pascale, The Morse-Sard theorem in Sobolev spaces. Indiana Univ. Math. J. 50 (2001) 1371–1386. [CrossRef] [Google Scholar]
  41. A. Figalli, A simple proof of the Morse-Sard theorem in Sobolev spaces. Proc. Am. Math. Soc. 136 (2008) 3675–3681. [CrossRef] [Google Scholar]
  42. C. Clason, V.H. Nhu and A. Rösch, Numerical analysis of a nonsmooth quasilinear elliptic control problem. I. Explicit second-order optimality conditions. (2022) Preprint. [Google Scholar]
  43. 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]
  44. M. Hinze, A variational discretization concept in control constrained optimization: the linear-quadratic case. Comput. Optim. Appl. 30 (2005) 45–61. [Google Scholar]
  45. E. Kammann, F. Tröltzsch and S. Volkwein, A posteriori error estimation for semilinear parabolic optimal control problems with application to model reduction by pod. ESAIM Math. Model. Numer. Anal. 47 (2013) 555–581. [CrossRef] [EDP Sciences] [MathSciNet] [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.