Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions

H. Frankowska

Annales de l'I.H.P. Analyse non linéaire (1985)

  • Volume: 2, Issue: 2, page 75-99
  • ISSN: 0294-1449

How to cite

top

Frankowska, H.. "Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions." Annales de l'I.H.P. Analyse non linéaire 2.2 (1985): 75-99. <http://eudml.org/doc/78093>.

@article{Frankowska1985,
author = {Frankowska, H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {derivative and "co-derivative" of set-valued mappings; differential inclusion; abstract optimization problem; Banach spaces; necessary optimality conditions},
language = {eng},
number = {2},
pages = {75-99},
publisher = {Gauthier-Villars},
title = {Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions},
url = {http://eudml.org/doc/78093},
volume = {2},
year = {1985},
}

TY - JOUR
AU - Frankowska, H.
TI - Adjoint differential inclusions in necessary conditions for the minimal trajectories of differential inclusions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 2
SP - 75
EP - 99
LA - eng
KW - derivative and "co-derivative" of set-valued mappings; differential inclusion; abstract optimization problem; Banach spaces; necessary optimality conditions
UR - http://eudml.org/doc/78093
ER -

References

top
  1. [1] J.P. Aubin, Applied Functional Analysis. 1979, Wiley Inter-Science. Zbl0424.46001MR549483
  2. [2] J.P. Aubin, F.H. Clarke, Shadow prices and duality for a class of optimal control problems. SIAM J. of Control, t. 17, no. 5, 1979, p. 567-586. Zbl0439.49018MR540838
  3. [3] J.P. Aubin, I. Ekeland, Applied Nonlinear Analysis, 1984, Wiley Interscience. Zbl0641.47066MR749753
  4. [4] J.P. Aubin and A. Cellina, Differential Inclusions, 1984, Springer-Verlag. Zbl0538.34007MR755330
  5. [5] F.H. Clarke, Generalized Gradient and Applications. Trans. Amer. Math. Soc., t. 205, 1975, p. 247-262. Zbl0307.26012MR367131
  6. [6] F.H. Clarke, The generalized problem of Bolza. SIAM J. of Control, t. 14, 1976, p. 682-699. Zbl0333.49023MR412926
  7. [7] F.H. Clarke, Optimal solutions to differential inclusions. J. Opt. Theory Appl., t. 19, no. 3, 1976, p. 469-478. Zbl0307.49042MR425714
  8. [8] F.H. Clarke, Optimization and Non-smooth Analysis, 1983. Wiley Interscience. Zbl0582.49001
  9. [9] I. Ekeland and R. Temam, Analyse convexe et problèmes variationels, 1974, Dunod, Paris. Zbl0281.49001MR463993
  10. [10] H. Frankowska, Contrôlabilité locale et propriétés des semi-groupes de correspondance, CRAS, t. 299, 1984 (Detailed version to appear). MR759223
  11. [11] H. Frankowska, C. Olech, Boundary solutions to differential inclusions. J. Diff. Eqs., t. 44, 1982, p. 156-165. Zbl0492.34053MR657776
  12. [12] A. Ioffe, Non-smooth analysis: differential calculus of nondifferentiable mappings. Trans. Amer. Math. Soc., t. 266, (1), 1981, p. 1-56. Zbl0651.58007
  13. [13] J.M. Lasry and H. Berliocchi, Principe de Pontriagin pour des systèmes régis par une equation différentielle multivoque. C. R. Acad. Sci., Paris, t. 277, 1973, p. 1103-1105. Zbl0282.49010MR353094
  14. [14] J.P. Penot and P. Terpolilli, Cônes tangents et singularités. C. R. Acad. Sci., Paris, t. 296, 1983, p. 721-724. Zbl0556.46026MR706667
  15. [15] L. Pontriagin, V. Boltyanskii, V. Gamkrelidze, E. Mischenko, The mathematical theory of optimal process, 1962. Wiley Interscience Publishers, New York. Zbl0102.32001MR166037
  16. [16] R.T. Rockafellar, Existence theorems for general control problems of Bolza and Lagrange. Adv. in Math. t. 15, 1975, p. 312-323. Zbl0319.49001MR365273
  17. [17] R.T. Rockafellar, Generalized directional derivatives and subgradients of non-convex functions. Canad. J. Math., t. 32, 1980, p. 257-280. Zbl0447.49009MR571922
  18. [18] R.T. Rockafellar, Convex analysis, 1970. Princeton University Press, Princeton, New Jersey. Zbl0193.18401MR274683
  19. [19] C. Ursescu, Tangent set's calculus and necessary conditions for extremality. SIAM J. of Control, t. 20, (4), 1982, p. 563-574. Zbl0488.49009MR661033
  20. [20] D.H. Wagner, Survey of measurable selection theorems. SIAM J. of Control, t. 15, 1977, p. 859-903. Zbl0407.28006MR486391
  21. [21] T. Ważewski, On an optimal control problem, Proc. Conference Differential equations and their applications, Prague, 1964, p. 229-242. Zbl0133.06005MR201758

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.