Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 100
Number of page(s) 52
DOI https://doi.org/10.1051/cocv/2025075
Published online 07 January 2026
  1. L. Cesari, Optimization Theory and Applications, Problems with Ordinary Differential Equations. Springer-Verlag, New York Inc. (1983). [Google Scholar]
  2. J.M. Longuski, J.J. Guzman and J.E. Prussing, Optimal Control with Aerospace Applications. Springer Science+Business Media, New York (2014). [Google Scholar]
  3. V. Pesce, A. Colagrossi and S. Silvestrini, Modern Spacecraft Guidance, Navigation and Control. Elsevier Inc. (2023). [Google Scholar]
  4. R. Yanushevsky, Modern Missile Guidance. CRC Press, Taylor & Francis Group (2019). [Google Scholar]
  5. N. Arada and J.-P. Raymond, Control problems with mixed control-state constraints. SIAM J. Control. Optim. 39 (2000) 1391-1407. [Google Scholar]
  6. N. Arada and J.-P. Raymond, Dirichlet boundary control of semilinear parabolic equations. Part 1. Problems with no state constraints. Appl. Math. Optim. 45 (2002) 125-143. [MathSciNet] [Google Scholar]
  7. N. Arada and J.-P. Raymond, Dirichlet boundary control of semilinear parabolic equations. Part 2. Problems with pointwise state constraints. Appl. Math. Optim. 45 (2002) 145-167. [Google Scholar]
  8. T. Bayen and F. Silva, Second order analysis for strong solution in the optimal control of parabolic equations. SIAM J. Control Optim. 54 (2016) 819-844. [Google Scholar]
  9. E. Casas, J.-P. Raymond and H. Zidani, Pontryagin's principle for local solutions of control problems with mixed control-state constraints. SIAM J. Control Optim,. 39 (2000) 1182-1203. [Google Scholar]
  10. G. Buskes and A.V. Rooij, Topological Spaces. From Distance to Neighiborhood. Springer (1996). [Google Scholar]
  11. 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]
  12. E. Casas and D. Wachsmuth, A Note on existence of solutions to control problems of semilinear partial differential equations. SIAM J. Control Optim. 61 (2023) 1095-1112. [Google Scholar]
  13. B. Hu and J. Yong, Pontryagin maximum principle for semilinear and quasilinear equations with pointwise state constraints. SIAM J. Control Optim. 33 (1995) 1857-1880. [Google Scholar]
  14. H. Khanh and B.T. Kien, On the regularity of multipliers and second-order optimality conditions of KKT-type for semilinear parabolic control problems. J. Math. Anal. Appl. 538 (2024) 128436. [Google Scholar]
  15. H. Khanh and B.T. Kien, Regularity of multipliers and second-order optimality conditions for semilinear parabolic optimal control problems with mixed pointwise constraints. Numer. Funct. Anal. Optim. 46 (2025) 137-165. [Google Scholar]
  16. F.J. Silva, Second order analysis for the optimal control of parabolic equations under control and final state constraints. Set-Valued Var. Anal. 24 (2016) 57-81. [Google Scholar]
  17. F. Troltzsch, Optimal Control of Partial Differential Equations, Theory, Method and Applications. American Mathematical Society, Providence Rhode Island (2010). [Google Scholar]
  18. H. Maurer and H.J. Oberle, Second order optimal conditions for optiamal control problems with free final time: the Riccati approach. SIAM J. Control Optim. 41 (2002) 380-403. [CrossRef] [MathSciNet] [Google Scholar]
  19. H. Maurer and N.P. Osmolovskii, Second order optimal conditions for time-optimal bang-bang control. SIAM J. Control Optim. 42 (2004) 2239-2263. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.-P. Raymond and H. Zidani, Pontryagin's principle for time-optimal problems. J. Optim. Theor. Appl. 101 (1999) 375-402. [Google Scholar]
  21. N. Arada and J.-P. Raymond, Time optimal problems with Dirichlet boundary controls. Discrete Continuous Dyn. Syst. 9 (2003) 1549-1570. [Google Scholar]
  22. L. Bonifacius, K. Pieper and B. Vexler, A priori estimates for space time-time finite element discretization of parabolic time-optimal problems. SIAM J. Control Optim. 57 (2019) 129-162. [Google Scholar]
  23. L. Tartar, An Introduction to Sobolev Spaces and Interpolation Spaces. Springer (2007). [Google Scholar]
  24. H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North Holland, Amsterdam (1978). [Google Scholar]
  25. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Pitman Publishing Inc. (1985). [Google Scholar]
  26. O. Ladyzhenskaya, V. Solonnikov and N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type. American Mathematical Society, Providence (1988). [Google Scholar]
  27. H. Brezis and P. Mironescu, Gagliardo-—Nirenberg inequalities and non-inequalities: the full story. Ann. Inst. Henri Poincare C 35 (2018) 1356. [Google Scholar]
  28. H. Amann, Linear and Quasilinear Parabolic Problems. Vol. II: Function Spaces. Birkhauser (2019). [Google Scholar]
  29. B.T. Kien and T.D. Binh, On the second-order optimality conditions for multi-objective optimal control problems with mixed pointwise constraints. J. Glob. Optim. 85 (2023) 155-183. [Google Scholar]
  30. W. Rudin, Functional Analysis. McGraw-Hill, Inc. (1973). [Google Scholar]
  31. A.D. Ioffe and V.M. Tihomirov, Theory of Extremal Problems. North-Holland, Amsterdam (1979). [Google Scholar]
  32. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, New York (2000). [Google Scholar]
  33. J.F. Bonnans and H. Zidani, Optimal control problems with partially polyhedric constraints. SIAM J. Control Optim. 37 (1999) 1726-1741. [Google Scholar]
  34. R. Cominetti, Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Optim. 21 (1990) 265-287. [Google Scholar]
  35. J. Zowe and S. Kurcyusz, Regularity and stability for the mathematical programming problem in Banach spaces. Appl. Math. Optim. 5 (1979) 49-62. [Google Scholar]
  36. A. Ben-Tal and J. Zowe, A unified theory of first and second order conditions for extremum problems in topological vector spaces. Math. Program. Study 19 (1982) 39-76. [Google Scholar]
  37. B.T. Kien and N.Q. Tuan, Error estimates for approximate solutions to seminlinear elliptic optimal control problems with nonlinear and mixed constraints. Numer. Funct. Anal. Optim. 43 (2022) 1672-1706. [Google Scholar]
  38. F. Troltzsch, Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations. Dynam. Contin. Discrete Impuls. Syst. 7 (2000) 289-306. [Google Scholar]
  39. F. Hirsch and G. Lacombe, Elements of Functional Analysis. Springer, New York (1999). [Google Scholar]
  40. Z. Pales and V. Zeidan, Characterization of Lx-closed decomposable set in L°°. J. Math. Anal. Appl. 238 (1999) 491-515. [Google Scholar]
  41. B.T. Kien, N.V. Tuyen and J.-C. Yao, Second-order KKT optimality conditions for multiobjective optimal control problems. SIAM J. Control Optim. 56 (2018) 4069-4097. [Google Scholar]
  42. L.C. Evans, Partial Differential Equations. AMS, Providence, Rhode Island (2010). [Google Scholar]
  43. B.T. Kien, V.H. Nhu and N.H. Son, Second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. Set-Valued Var. Anal. 25 (2017) 177-210. [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.