An implicit-function theorem for a class of monotone generalized equations
Kybernetika, Tome 29 (1993) no. 3, pp. 210-221 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 26B10, 26E25, 47H04, 47H15, 47H19, 49J40, 49K40, 54C60
@article{KYB_1993_29_3_a1,
     author = {Alt, Walter and Kolumb\'an, Iosif},
     title = {An implicit-function theorem for a class of monotone generalized equations},
     journal = {Kybernetika},
     pages = {210--221},
     year = {1993},
     volume = {29},
     number = {3},
     mrnumber = {1231867},
     zbl = {0792.49005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1993_29_3_a1/}
}
TY  - JOUR
AU  - Alt, Walter
AU  - Kolumbán, Iosif
TI  - An implicit-function theorem for a class of monotone generalized equations
JO  - Kybernetika
PY  - 1993
SP  - 210
EP  - 221
VL  - 29
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/KYB_1993_29_3_a1/
LA  - en
ID  - KYB_1993_29_3_a1
ER  - 
%0 Journal Article
%A Alt, Walter
%A Kolumbán, Iosif
%T An implicit-function theorem for a class of monotone generalized equations
%J Kybernetika
%D 1993
%P 210-221
%V 29
%N 3
%U http://geodesic.mathdoc.fr/item/KYB_1993_29_3_a1/
%G en
%F KYB_1993_29_3_a1
Alt, Walter; Kolumbán, Iosif. An implicit-function theorem for a class of monotone generalized equations. Kybernetika, Tome 29 (1993) no. 3, pp. 210-221. http://geodesic.mathdoc.fr/item/KYB_1993_29_3_a1/

[1] W. Alt: The Lagrange-Newton method for infinite-dimensional optimization problems. Numer. Funct. Anal. Optim. 11 (1990), 201-224. | MR | Zbl

[2] W. Alt: Parametric programming with applications to optimal control and sequential quadratic programming. Bayreuther Mathematische Schriften 35 (1991), 1-37. | MR

[3] J.-P. Aubin, I. Ekeland: Applied Nonlinear Analysis. J. Wiley, New York 1984. | MR | Zbl

[4] J.-P. Aubin, H. Frankowska: Set-valued Analysis. Birkhauser, Boston 1990. | MR | Zbl

[5] F. E. Browder: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces. Amer. Math. Soc, Providence, Rhode Island 1976. | MR | Zbl

[6] S. Dafermos: Sensitivity analysis in variational inequalities. Math. Oper. Res. IS (1988), 421-434. | MR | Zbl

[7] A. V. Fiacco: Sensitivity analysis for nonlinear programming using penalty methods. Math. Programming 10 (1976), 287-311. | MR | Zbl

[8] A. V. Fiacco: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming. Academic Press, New York - London 1983. | MR | Zbl

[9] A. D. Ioffe, V. M. Tihomirov: Theory of Extremal Problems. North-Holland, Amsterdam - New York - Oxford 1979. | MR | Zbl

[10] K. Ito, K. Kunisch: Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimation. Preprint, 1989. | MR

[11] G. Kassay, I. Kolumban: Implicit-function theorems for monotone mappings. Research Seminar on Mathematical Analysis, Babes-Bolyai University, Preprint Nr. 6 (1988), 7-24. | MR | Zbl

[12] G. Kassay, I. Kolumban: Implicit functions and variational inequalities for monotone mappings. Research Seminar on Mathematical Analysis, Babes-Bolyai University, Preprint Nr.7 (1989), 79-92. | MR | Zbl

[13] K. Malanowski: Second-order conditions and constraint qualifications in stability and sensitivity analysis of solutions to optimization problems in Hilbert spaces. Appl. Math. Optim. (to appear). | MR | Zbl

[14] G. Minty: Monotone (nonlinear) operators in Hilbert spaces. Duke Math. J. 29 (1962), 341-346. | MR

[15] S. M. Robinson: Strongly regular generalized equations. Math. Oper. Res. 5 (1980), 43-62. | MR | Zbl

[16] S. M. Robinson: Generalized equations. In: Mathematical Programming - The State of the Art (A. Bachem, M. Grotschel, B. Korte eds.), Springer-Verlag, Berlin 1983, pp. 346-368. | MR | Zbl

[17] S. M. Robinson: An implicit-function theorem for a class of nonsmooth functions. Math. Oper. Res. 16 (1991), 292-309. | MR | Zbl

[18] R. T. Rockafellar: On the maximality of sums of nonlinear monotone operators. Trans. Amer. Math. Soc. 149 (1970), 75-88. | MR | Zbl