Free Access
Volume 14, Number 4, October-December 2008
Page(s) 825 - 863
Published online 07 February 2008
  1. E.L. Allgower and K. Georg, Numerical continuation methods, Springer Series in Computational Mathematics 13. Springer-Verlag, Berlin (1990).
  2. 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).
  3. P. Berkmann and H.J. Pesch, Abort landing in windshear: optimal control problem with third-order state constraint and varied switching structure. J. Optim. Theory Appl. 85 (1995) 21–57. [CrossRef] [MathSciNet]
  4. J.F. Bonnans and A. Hermant, Conditions d'optimalité du second ordre nécessaires ou suffisantes pour les problèmes de commande optimale avec une contrainte sur l'état et une commande scalaires. C. R. Math. Acad. Sci. Paris 343 (2006) 473–478. [CrossRef] [MathSciNet]
  5. J.F. Bonnans and A. Hermant, Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints. Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear).
  6. J.F. Bonnans and A. Hermant, Well-posedness of the shooting algorithm for state constrained optimal control problems with a single constraint and control. SIAM J. Control Optim. 46 (2007) 1398–1430. [CrossRef] [MathSciNet]
  7. J.F. Bonnans and A. Hermant, No gap second order optimality conditions for optimal control problems with a single state constraint and control. Math. Programming, Ser. B (2007) DOI: 10.1007/s10107-007-0167-8.
  8. J.F. Bonnans and A. Shapiro, Perturbation analysis of optimization problems. Springer-Verlag, New York (2000).
  9. A.E. Bryson, W.F. Denham and S.E. Dreyfus, Optimal programming problems with inequality constraints I: Necessary conditions for extremal solutions. AIAA Journal 1 (1963) 2544–2550. [CrossRef]
  10. R. Bulirsch, F. Montrone and H.J. Pesch, Abort landing in the presence of windshear as a minimax optimal control problem. II. Multiple shooting and homotopy. J. Optim. Theory Appl. 70 (1991) 223–254. [CrossRef] [MathSciNet]
  11. P. Deuflhard, Newton methods for nonlinear problems, Affine invariance and adaptive algorithms, Springer Series in Computational Mathematics 35. Springer-Verlag, Berlin (2004).
  12. A.L. Dontchev and W.W. Hager, Lipschitzian stability for state constrained nonlinear optimal control. SIAM J. Control Optim. 36 (1998) 698–718 (electronic). [CrossRef] [MathSciNet]
  13. N. Dunford and J. Schwartz, Linear operators, Vols. I and II. Interscience, New York (1958), (1963).
  14. J. Gergaud and T. Haberkorn, Homotopy method for minimum consumption orbit transfer problem. ESAIM: COCV 12 (2006) 294–310 (electronic). [CrossRef] [EDP Sciences]
  15. W.W. Hager, Lipschitz continuity for constrained processes. SIAM J. Control Optim. 17 (1979) 321–338. [CrossRef] [MathSciNet]
  16. A. Haraux, How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities. J. Math. Soc. Japan 29 (1977) 615–631. [CrossRef] [MathSciNet]
  17. R.F. Hartl, S.P. Sethi and R.G. Vickson, A survey of the maximum principles for optimal control problems with state constraints. SIAM Review 37 (1995) 181–218. [CrossRef] [MathSciNet]
  18. A.D. Ioffe and V.M. Tihomirov, Theory of Extremal Problems. North-Holland Publishing Company, Amsterdam (1979). Russian Edition: Nauka, Moscow (1974).
  19. D.H. Jacobson, M.M. Lele and J.L. Speyer, New necessary conditions of optimality for control problems with state-variable inequality contraints. J. Math. Anal. Appl. 35 (1971) 255–284. [CrossRef] [MathSciNet]
  20. K. Malanowski, Two-norm approach in stability and sensitivity analysis of optimization and optimal control problems. Adv. Math. Sci. Appl. 2 (1993) 397–443. [MathSciNet]
  21. K. Malanowski, Stability and sensitivity of solutions to nonlinear optimal control problems. J. Appl. Math. Optim. 32 (1995) 111–141. [CrossRef]
  22. K. Malanowski, Sufficient optimality conditions for optimal control subject to state constraints. SIAM J. Control Optim. 35 (1997) 205–227. [CrossRef] [MathSciNet]
  23. K. Malanowski and H. Maurer, Sensitivity analysis for state constrained optimal control problems. Discrete Contin. Dynam. Systems 4 (1998) 241–272. [CrossRef] [MathSciNet]
  24. P. Martinon and J. Gergaud, An application of PL continuation methods to singular arcs problems, in Recent advances in optimization, Lect. Notes Econom. Math. Systems 563, Springer, Berlin (2006) 163–186.
  25. H. Maurer, On the minimum principle for optimal control problems with state constraints. Schriftenreihe des Rechenzentrum 41, Universität Münster (1979).
  26. H. Maurer and H.J. Pesch, Solution differentiability for nonlinear parametric control problems. SIAM J. Control Optim. 32 (1994) 1542–1554. [CrossRef] [MathSciNet]
  27. F. Mignot, Contrôle dans les inéquations variationnelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [CrossRef]
  28. 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; L.W. Neustadt Ed., Interscience Publishers John Wiley & Sons, Inc. New York-London (1962).
  29. S.M. Robinson, First order conditions for general nonlinear optimization. SIAM J. Appl. Math. 30 (1976) 597–607. [CrossRef] [MathSciNet]
  30. S.M. Robinson, Stability theorems for systems of inequalities, part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13 (1976) 497–513. [CrossRef] [MathSciNet]
  31. S.M. Robinson, Strongly regular generalized equations. Math. Oper. Res. 5 (1980) 43–62. [CrossRef] [MathSciNet]
  32. J. Sokolowski, Sensitivity analysis of control constrained optimal control problems for distributed parameter systems. SIAM J. Control Optim. 25 (1987) 1542–1556. [CrossRef] [MathSciNet]
  33. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis. Springer-Verlag, New York (1993).

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