High order inverse function theorems

H. Frankowska

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: S6, page 283-303
  • ISSN: 0294-1449

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Frankowska, H.. "High order inverse function theorems." Annales de l'I.H.P. Analyse non linéaire S6 (1989): 283-303. <http://eudml.org/doc/78199>.

@article{Frankowska1989,
author = {Frankowska, H.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {reachable set; stability; inverse mapping theorems; complete metric space},
language = {eng},
pages = {283-303},
publisher = {Gauthier-Villars},
title = {High order inverse function theorems},
url = {http://eudml.org/doc/78199},
volume = {S6},
year = {1989},
}

TY - JOUR
AU - Frankowska, H.
TI - High order inverse function theorems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - S6
SP - 283
EP - 303
LA - eng
KW - reachable set; stability; inverse mapping theorems; complete metric space
UR - http://eudml.org/doc/78199
ER -

References

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  1. [1] Aubin J.-P. (1982) Comportement lipschitzien des solutions de problèmes de minimisation convexes. CRAS, Paris, 295, 235-238 Zbl0503.49022MR681586
  2. [2] Aubin J.-P. (1984) Lipschitz behavior of solutions to convex minimization problems. Math. Operations Research, 8, 87-111 Zbl0539.90085MR736641
  3. [3] Aubin J.-P. & Cellina A. (1984) DIFFERENTIAL INCLUSIONS. Springer Verlag Zbl0538.34007
  4. [4] Aubin J.-P. & Ekeland I. (1984) APPLIED NONLINEAR ANALYSIS. Wiley-Interscience Zbl0641.47066
  5. [5] Aubin J.-P. & Frankowska H. (1987) On the inverse function theorem. J. Math. Pures & Appliquées, 66, 71-89 Zbl0643.46033
  6. [6] Ambrosetti A. & Prodi G. (1973) On the inversion of some differential mappings with singularities between Banach spaces. Ann. Math. Pure Appl., 93, 231-247 Zbl0288.35020
  7. [7] Beauzamy P. (1985) INTRODUCTION TO BANACH SPACES AND THEIR GEOMETRY. North Holland, Math. Study, 68 Zbl0585.46009MR889253
  8. [8] Clarke F.H. (1983) OPTIMIZATION AND NONSMOOTH ANALYSIS. Wiley-Interscience Zbl0582.49001MR709590
  9. [9] Dmitruk A.V., Milyutin A.A. & Osmolovskii N.P. (1980) Ljusternik's theorem and the theory of extrema. Uspekhi Mat. Nauk, 35:6, 11-46 / Russian Math Surveys, 35:6, 11-51 Zbl0479.49015
  10. [10] Ekeland I. (1979) Nonconvex minimization problems. Bull. Am. Math. Soc., 1, 443-474 Zbl0441.49011MR526967
  11. [11] Fattorini H. (1987) A unified theory of necessary conditions for nonlinear nonconvex systems. Appl. Math. & Opt., 2, 141-184 Zbl0616.49015
  12. [12] Fattorini H. & Frankowska H. (to appear) Necessary conditions for infinite dimensional control problems. Zbl0737.49017
  13. [13] Frankowska H. (1986) Théorème d'application ouverte pour des correspondances. CRAS, Paris302, 559-562 Zbl0588.49008MR845648
  14. [14] Frankowska H. (1987) An open mapping principle for set-valued maps.J. Math. Analysis & Appl., 127, 172-180 Zbl0643.46034
  15. [15] Frankowska H. (1987) Local controllability and infinitesimal generators of semigroups of set-valued maps. SIAM J. Control & Optimization, 25, 412- 432 Zbl0625.49015
  16. [16] Frankowska H. (1987) Théorèmes d'application ouverte et de fonction inverse. CRAS, Paris, 305, 773-776 Zbl0635.46041MR921132
  17. [17] Frankowska H. (1989) Local controllability of control systems with feedbacks. J. Opt. Th. & Appl., n° 2, (to appear) Zbl0633.93013
  18. [18] Frankowska H. (to appear) On the linearization of nonlinear control systems and exact reachability. Proceedings of IFIP Conference on Optimal Control of Systems Governed by Partial Differential Equations, Santiago de Compostela, Spain, July 6-9, 1987, Springer Verlag Zbl0677.93042MR987973
  19. [19] Frankowska H.Some Inverse Mapping Theorems. (to appear) Zbl0727.26014
  20. [20] Graves L.M. (1950) Some mapping theorem. Duke Math. J., 17, 111-114 Zbl0037.20401MR35398
  21. [21] Ioffe A.D. (1987) On the local surjection property. J. Nonlinear Analysis, 11, 565-592 Zbl0642.49010MR886649
  22. [22] Ioffe A.D. & Tikhomirov V.M. (1974) THEORY OF EXTREMAL PROBLEMS. Nauka, Moskow 
  23. [23] Ljusternik L.A. (1934) Conditional extrema of functionals. Mat. Sb., 41, 390-401 
  24. [24] Mangasarian O.L., & Fromovitz S. (1967) The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J. Math. Analysis & Appl., 17, 37-47 Zbl0149.16701
  25. [25] Robinson S. (1976) Stability theory for systems of inequalities, part II: differentiable nonlinear systems. SIAM J. Numerical Analysis, 13, 497-513 Zbl0347.90050MR410522
  26. [26] Rockafellar R.T. (1986) Lipschitzian stability in optimization: the role of nonsmooth analysis. IIASA WP-8646 Zbl0586.49012MR822004
  27. [27] Rockafellar R.T. (1987) Second-order optimality conditions in nonlinear programming obtained by way of pseudo-derivatives. (preprint) 

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