High order inverse function theorems
Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), pp. 283-303. 
@article{AIHPC_1989__S6__283_0,
     author = {Frankowska, H.},
     title = {High order inverse function theorems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {283--303},
     publisher = {Gauthier-Villars},
     volume = {S6},
     year = {1989},
     mrnumber = {1019118},
     zbl = {0701.49040},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1989__S6__283_0/}
}
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Frankowska, H. High order inverse function theorems. Annales de l'I.H.P. Analyse non linéaire, Tome S6 (1989), pp. 283-303. http://www.numdam.org/item/AIHPC_1989__S6__283_0/

[1] Aubin J.-P. (1982) Comportement lipschitzien des solutions de problèmes de minimisation convexes. CRAS, Paris, 295, 235-238 | MR | Zbl

[2] Aubin J.-P. (1984) Lipschitz behavior of solutions to convex minimization problems. Math. Operations Research, 8, 87-111 | MR | Zbl

[3] Aubin J.-P. & Cellina A. (1984) DIFFERENTIAL INCLUSIONS. Springer Verlag | Zbl

[4] Aubin J.-P. & Ekeland I. (1984) APPLIED NONLINEAR ANALYSIS. Wiley-Interscience | Zbl

[5] Aubin J.-P. & Frankowska H. (1987) On the inverse function theorem. J. Math. Pures & Appliquées, 66, 71-89 | Zbl

[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 | Zbl

[7] Beauzamy P. (1985) INTRODUCTION TO BANACH SPACES AND THEIR GEOMETRY. North Holland, Math. Study, 68 | MR | Zbl

[8] Clarke F.H. (1983) OPTIMIZATION AND NONSMOOTH ANALYSIS. Wiley-Interscience | MR | Zbl

[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 | Zbl

[10] Ekeland I. (1979) Nonconvex minimization problems. Bull. Am. Math. Soc., 1, 443-474 | MR | Zbl

[11] Fattorini H. (1987) A unified theory of necessary conditions for nonlinear nonconvex systems. Appl. Math. & Opt., 2, 141-184 | Zbl

[12] Fattorini H. & Frankowska H. (to appear) Necessary conditions for infinite dimensional control problems. | Zbl

[13] Frankowska H. (1986) Théorème d'application ouverte pour des correspondances. CRAS, Paris 302, 559-562 | MR | Zbl

[14] Frankowska H. (1987) An open mapping principle for set-valued maps. J. Math. Analysis & Appl., 127, 172-180 | Zbl

[15] Frankowska H. (1987) Local controllability and infinitesimal generators of semigroups of set-valued maps. SIAM J. Control & Optimization, 25, 412- 432 | Zbl

[16] Frankowska H. (1987) Théorèmes d'application ouverte et de fonction inverse. CRAS, Paris, 305, 773-776 | MR | Zbl

[17] Frankowska H. (1989) Local controllability of control systems with feedbacks. J. Opt. Th. & Appl., n° 2, (to appear) | Zbl

[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 | MR | Zbl

[19] Frankowska H. Some Inverse Mapping Theorems. (to appear) | Numdam | Zbl

[20] Graves L.M. (1950) Some mapping theorem. Duke Math. J., 17, 111-114 | MR | Zbl

[21] Ioffe A.D. (1987) On the local surjection property. J. Nonlinear Analysis, 11, 565-592 | MR | Zbl

[22] Ioffe A.D. & Tikhomirov V.M. (1974) THEORY OF EXTREMAL PROBLEMS. Nauka, Moskow

[23] Ljusternik L.A. (1934) Conditional extrema of functionals. Mat. Sb., 41, 390-401

[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 | Zbl

[25] Robinson S. (1976) Stability theory for systems of inequalities, part II: differentiable nonlinear systems. SIAM J. Numerical Analysis, 13, 497-513 | MR | Zbl

[26] Rockafellar R.T. (1986) Lipschitzian stability in optimization: the role of nonsmooth analysis. IIASA WP-8646 | MR | Zbl

[27] Rockafellar R.T. (1987) Second-order optimality conditions in nonlinear programming obtained by way of pseudo-derivatives. (preprint)