EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 20 / No 3 (July-September 2014) ESAIM: COCV, 20 3 (2014) 704-724 References
Free Access
Issue
ESAIM: COCV
Volume 20, Number 3, July-September 2014
Page(s) 704 - 724
DOI https://doi.org/10.1051/cocv/2013080
Published online 14 March 2014
  1. L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York (2000). [Google Scholar]
  2. J.F. Bonnans, X. Dupuis and L. Pfeiffer, Second-order necessary conditions in Pontryagin form for optimal control problems. Inria Research Report RR-8306. INRIA (2013). [Google Scholar]
  3. J.F. Bonnans and A. Hermant, No-gap second-order optimality conditions for optimal control problems with a single state constraint and control. Math. Program. B 117 (2009) 21–50. [Google Scholar]
  4. J.F. Bonnans and A. Hermant, Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints. Ann. Inst. Henri Poincaré Anal. Non Linéaire 26 (2009) 561–598. [Google Scholar]
  5. J.F. Bonnans and N.P. Osmolovskiĭ, Second-order analysis of optimal control problems with control and initial-final state constraints. J. Convex Anal. 17 (2010) 885–913. [Google Scholar]
  6. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer Series in Operations Research. Springer-Verlag, New York (2000). [Google Scholar]
  7. R. Cominetti, Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Opt. 21 (1990) 265–287. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.V. Dmitruk, Maximum principle for the general optimal control problem with phase and regular mixed constraints. Software and models of systems analysis. Optimal control of dynamical systems. Comput. Math. Model. 4 (1993) 364–377. [CrossRef] [MathSciNet] [Google Scholar]
  9. A.Ja. Dubovickiĭ and A.A. Miljutin, Extremal problems with constraints. Ž. Vyčisl. Mat. i Mat. Fiz. 5 (1965) 395–453. [Google Scholar]
  10. A.Ja. Dubovickiĭ and A.A. Miljutin, Necessary conditions for a weak extremum in optimal control problems with mixed constraints of inequality type. Ž. Vyčisl. Mat. i Mat. Fiz. 8 (1968) 725–779. [Google Scholar]
  11. M.R. Hestenes, Calculus of variations and optimal control theory. John Wiley & Sons Inc., New York (1966). [Google Scholar]
  12. R.P. Hettich and H.Th. Jongen, Semi-infinite programming: conditions of optimality and applications, in Optimization techniques, Proc. 8th IFIP Conf., Würzburg 1977, Part 2. Vol. 7 of Lecture Notes in Control and Information Sci. Springer, Berlin (1978) 1–11. [Google Scholar]
  13. H. Kawasaki, An envelope-like effect of infinitely many inequality constraints on second-order necessary conditions for minimization problems. Math. Program. 41 (Ser. A) (1988) 73–96. [CrossRef] [Google Scholar]
  14. K. Malanowski and H. Maurer, Sensitivity analysis for optimal control problems subject to higher order state constraints. Optimization with data perturbations II. Ann. Oper. Res. 101 (2001) 43–73. [CrossRef] [Google Scholar]
  15. H. Mäurer, First and second order sufficient optimality conditions in mathematical programming and optimal control. Math. Program. Oberwolfach Proc. Conf. Math. Forschungsinstitut, Oberwolfach (1979). Math. Programming Stud. 14 (1981) 163–177. [CrossRef] [Google Scholar]
  16. 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). [Google Scholar]
  17. N.P. Osmolovskii, Quadratic extremality conditions for broken extremals in the general problem of the calculus of variations. Optimal control and dynamical systems. J. Math. Sci. 123 (2004) 3987–4122. [CrossRef] [MathSciNet] [Google Scholar]
  18. N.P. Osmolovskii, Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints. J. Math. Sci., 173 (2011) 1–106. [CrossRef] [MathSciNet] [Google Scholar]
  19. N.P. Osmolovskii, Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints. ESAIM: COCV 18 (2012) 452–482. [CrossRef] [EDP Sciences] [Google Scholar]
  20. N.P. Osmolovskii and H. Maurer, Applications to regular and bang-bang control, vol. 24 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2012). [Google Scholar]
  21. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes. Translated from the Russian by K.N. Trirogoff, edited by L.W. Neustadt. Interscience Publishers John Wiley & Sons, Inc. New York-London (1962). [Google Scholar]
  22. G. Stefani and P. Zezza, Optimality conditions for a constrained control problem. SIAM J. Control Optim 34 (1996) 635–659. [CrossRef] [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.