Some inverse mapping theorems
Annales de l'I.H.P. Analyse non linéaire (1990)
- Volume: 7, Issue: 3, page 183-234
- ISSN: 0294-1449
Access Full Article
topHow to cite
topFrankowska, Hélène. "Some inverse mapping theorems." Annales de l'I.H.P. Analyse non linéaire 7.3 (1990): 183-234. <http://eudml.org/doc/78221>.
@article{Frankowska1990,
author = {Frankowska, Hélène},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {inverse mapping theorems; set-valued maps; open mapping principle; controllability; finite and infinite dimensional control systems; optimality; implicit function theorem; stability of constraints; nonsmooth analysis},
language = {eng},
number = {3},
pages = {183-234},
publisher = {Gauthier-Villars},
title = {Some inverse mapping theorems},
url = {http://eudml.org/doc/78221},
volume = {7},
year = {1990},
}
TY - JOUR
AU - Frankowska, Hélène
TI - Some inverse mapping theorems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 3
SP - 183
EP - 234
LA - eng
KW - inverse mapping theorems; set-valued maps; open mapping principle; controllability; finite and infinite dimensional control systems; optimality; implicit function theorem; stability of constraints; nonsmooth analysis
UR - http://eudml.org/doc/78221
ER -
References
top- [1] J.-P. Aubin, Lipschitz Behavior of Solutions to Convex Minimization Problems, Math. Operat. Res., Vol. 9, 1984, pp. 87-111. Zbl0539.90085MR736641
- [2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag (Grundlehren der Math. Wissenscharften), Vol. 264, 1984. Zbl0538.34007MR755330
- [3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Berlin, Boston, 1990. Zbl0713.49021MR1048347
- [4] J.-P. Aubin and H. Frankowska, On inverse function theorems for set-valued maps, J. Math. Pure Appl., Vol. 66, 1987, pp. 71-89. Zbl0643.46033MR884814
- [5] P. Beauzamy, Introduction to Banach spaces and their Geometry, North HollandMathematics study, Vol. 68, 1985. Zbl0585.46009MR889253
- [6] R.M. Bianchini and G. Stefani, Sufficient Conditions of Local Controllability, Preprint Istituto Matematico Ulisse Dini1986.
- [7] J.F. Bonnans and E. Casas, Optimal Control of Semilinear Multistate Systems with State Constraints, SIAM J, Control Optimi., Vol. 27, 1989, pp. 446-455. Zbl0667.49014MR984837
- [8] F F. Clarke,On the Inverse Function Theorem, Pac. J. Math., Vol. 64, 1976, pp. 97- 102. Zbl0331.26013MR425047
- [9] F. Clarke, Optimization and Nonsmooth Analysis, WileyInterscience, 1983. Zbl0582.49001MR709590
- [10] B.D. Craven and M.Z. Nashed, Generalized Implicit Function Theorems when the Derivative has no Bounded Inverse, Nonlinear Analysis, Vol. 6, 1982, pp. 375-387. Zbl0486.58004MR654813
- [11] A.V. Dmitruk, A.A. Milyutin and N.P. Osmolovskii, Ljustemik's Theorem and the Theory of Extrema, Uspekhi Mat. Nauk., Vol. 35:6, 1980, pp. 11-46; Russian Math. Surveys, Vol. 35:6, 1980, pp. 11-51. Zbl0479.49015MR601755
- [12] I. Ekeland, On the Variational Principle, J. Math. Anal. Appl., Vol. 47, 1974, pp. 324- 358. Zbl0286.49015MR346619
- [13] I. Ekeland, Nonconvex Minimization Problems, Bull. Am. Math. Soc., Vol. 1, 1979, pp. 443-474. Zbl0441.49011MR526967
- [14] H. Fattorini, A Unified Theory of Necessary Conditions for Nonlinear Non-convex Control Systems, Applied Math. Optimiz., Vol. 15, 1986, pp. 141-185. Zbl0616.49015MR868904
- [15] H. Fattorini and H. Frankowska, Necessary Conditions for Infinite Dimensional Control Problems, Mathematics of Systems, Signals and Control, 1991. Zbl0737.49017MR1082855
- [16] H. Frankowska, Théorèmes d'application ouverte et de fonction inverse, C. R. Acad. Sci., Paris, Vol. 305, 1987, pp. 773-776. Zbl0635.46041MR921132
- [17] H. Frankowska, High Order Inverse Function Theorems, Analyse non linéaire, Proceedings of the Conference on Applied Nonlinear Analysis, Perpignan, June 22-26, 1987, Gauthier-Villars, Paris, 1989.
- [18] H. Frankowska, An Open Mapping Principle for Set-valued Maps, J. Math. Anal. Appl., Vol. 127, 1987, pp. 172-180. Zbl0643.46034MR904219
- [19] H. Frankowska, Local Controllability of Control Systems with Feedback, J. Optimiz. Theor. Appl., Vol. 60, 1989, pp. 277-296. Zbl0633.93013MR984985
- [20] H. Frankowska, Local Controllability and Infinitesimal Generators of Semi-groups of Set-valued Maps, SIAM J., Control Optimiz., Vol. 25, 1987, pp. 412-432. Zbl0625.49015MR877070
- [21] H. Frankowska, The Maximum Principle for an Optimal Solution to a Differential Inclusion with end Point Constraints, SIAM J., Control Optimiz., Vol. 25, 1987, pp. 145-157. Zbl0614.49017MR872456
- [22] H. Frankowska, The First Order Necessary Conditions for Nonsmooth Variational and Control Problems, SIAM J., Control Optimiz., Vol. 22, 1984, pp. 1-12. Zbl0529.49011MR728668
- [23] H. Frankowska, Set-valued Analysis and Some Control Problems, Modem Optimal Control, Proceedings of the International Conference "30 years of Modern Control Theory", Kingston, June 3-6, 1988, E. Roxin Editor, Marcel Dekker, New York, Basel, 1989. Zbl0702.49013MR1013205
- [24] L.M. Graves, Some Mapping Theorem, Duke Math. J., Vol. 17, 1950, pp. 111-114. Zbl0037.20401MR35398
- [25] K. Grasse, A Higher-order Sufficient Condition for Local Surjectivity, Nonlinear Analysis, Vol. 10, 1986, pp. 87-96. MR820660
- [26] A.D. Ioffe, Regular Points of Lipschitz Functions, Trans. Am. Math. Soc., Vol. 251, 1979, pp. 61-69. Zbl0427.58008MR531969
- [27] A.D. Ioffe, Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings, Trans. Am. Math. Soc., 266, 1981, pp. 1-56. Zbl0651.58007MR613784
- [28] A.E. Ioffe, On the Local Surjection property, Nonlinear Analysis, Vol. 11, 1987, pp. 565-592. Zbl0642.49010MR886649
- [29] C. Kuratowski, Topologie, Panstwowe Wydawnictwo Naukowe, 1958. Zbl0078.14603MR90795
- [30] E.B. Lee and L. Markus, Foundations of Optimal Control Theory. John Wiley, New York1967. Zbl0159.13201MR220537
- [31] L.A. Ljusternik, Conditional Extrema of Functionals, Mat. Sb., Vol. 41, 1934, pp. 390-401.
- [32] L.A. Ljusternik and V.I. Sobolev, Elementy Funktsionalnogo Analiza, Second ed., NaukaMoskow, 1965 (in Russian). MR209802
- [33] K. Magnusson, A.J. Pritchard and M.D. Quinn, The Application of Fixed Point to Global Nonlinear Controllability Problems, Mathematical Control Theory, Banach Center Publications, Vol. 14, 1985, pp. 319-344. Zbl0576.93009MR851235
- [34] K. Magnusson and A.J. Pritchard, Local Exact Controllability of Non-linear Evolution Equations, Recent Advances in Differential Equations, Academic Press, 1981, Vol. 271, pp. 271-280. Zbl0598.34054MR643139
- [35] J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. MR227584
- [36] A. Pazy, Semi-groups of linear operators and applications to partial differential equations, Spinger, Berlin, 1978.
- [37] S. Robinson, Perturbed Kuhn-Tucker Points and Rates of Convergence for a Class of Nonlinear-programming Algorithms, Math. Programming, Vol. 7, 1974, pp. 1-16. Zbl0294.90078MR368787
- [38] R.T. Rockafellar, Lipschitzian Properties of Multifunctions, Non-linear Analysis, T.M.A., 9, 1985, pp. 867-885. Zbl0573.54011MR799890
- [39] H. Sussmann, A Sufficient Condition for Local Controllability, SIAM J., Control Optimiz., Vol. 16, 1978, pp. 790-802. Zbl0391.93004MR527718
- [40] J. Treiman, Characterization of Clarke's Tangent and Normal Cones in Finite and Infinite Dimension, Nonlinear Analysis, Vol. 7, 1983, pp. 771-783. Zbl0515.49013MR707085
- [41] J. Warga, Necessary Conditions Without Differentiability Assumptions in Optimal Control, J. Differ. Equations, Vol. 18, 1975, pp. 41-62. Zbl0272.49005MR377655
- [42] J. Warga, Derivate Containers, Inverse Functions and Controllability, in Calculus of Variations and Control Theory, D. L. RUSSEL, Ed., Academic Press, New York, 1976, pp. 13-46. Zbl0355.26004MR427561
- [43] J. Warga, Optimization and Controllability Without Differentiability Assumptions, SIAM J. Control Optimiz., Vol. 21, 1983, pp. 837-855. Zbl0526.49026MR719516
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.