| Title:
|
An implicit-function theorem for a class of monotone generalized equations (English) |
| Author:
|
Alt, Walter |
| Author:
|
Kolumbán, Iosif |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
29 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
210-221 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26B10 |
| MSC:
|
26E25 |
| MSC:
|
47H04 |
| MSC:
|
47H15 |
| MSC:
|
47H19 |
| MSC:
|
49J40 |
| MSC:
|
49K40 |
| MSC:
|
54C60 |
| idZBL:
|
Zbl 0792.49005 |
| idMR:
|
MR1231867 |
| . |
| Date available:
|
2009-09-24T18:40:04Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125106 |
| . |
| Reference:
|
[1] W. Alt: The Lagrange-Newton method for infinite-dimensional optimization problems.Numer. Funct. Anal. Optim. 11 (1990), 201-224. Zbl 0694.49022, MR 1068833 |
| Reference:
|
[2] W. Alt: Parametric programming with applications to optimal control and sequential quadratic programming.Bayreuther Mathematische Schriften 35 (1991), 1-37. MR 1104518 |
| Reference:
|
[3] J.-P. Aubin, I. Ekeland: Applied Nonlinear Analysis.J. Wiley, New York 1984. Zbl 0641.47066, MR 0749753 |
| Reference:
|
[4] J.-P. Aubin, H. Frankowska: Set-valued Analysis.Birkhauser, Boston 1990. Zbl 0713.49021, MR 1048347 |
| Reference:
|
[5] F. E. Browder: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces.Amer. Math. Soc, Providence, Rhode Island 1976. Zbl 0327.47022, MR 0405188 |
| Reference:
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[6] S. Dafermos: Sensitivity analysis in variational inequalities.Math. Oper. Res. IS (1988), 421-434. Zbl 0674.49007, MR 0961802 |
| Reference:
|
[7] A. V. Fiacco: Sensitivity analysis for nonlinear programming using penalty methods.Math. Programming 10 (1976), 287-311. Zbl 0357.90064, MR 0434444 |
| Reference:
|
[8] A. V. Fiacco: Introduction to Sensitivity and Stability Analysis in Nonlinear Programming.Academic Press, New York - London 1983. Zbl 0543.90075, MR 0721641 |
| Reference:
|
[9] A. D. Ioffe, V. M. Tihomirov: Theory of Extremal Problems.North-Holland, Amsterdam - New York - Oxford 1979. Zbl 0407.90051, MR 0528295 |
| Reference:
|
[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 1178394 |
| Reference:
|
[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. Zbl 0664.46045, MR 0989594 |
| Reference:
|
[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. Zbl 0724.47027, MR 1043190 |
| Reference:
|
[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). Zbl 0756.90093, MR 1133252 |
| Reference:
|
[14] G. Minty: Monotone (nonlinear) operators in Hilbert spaces.Duke Math. J. 29 (1962), 341-346. MR 0169064 |
| Reference:
|
[15] S. M. Robinson: Strongly regular generalized equations.Math. Oper. Res. 5 (1980), 43-62. Zbl 0437.90094, MR 0561153 |
| Reference:
|
[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. Zbl 0554.34007, MR 0717407 |
| Reference:
|
[17] S. M. Robinson: An implicit-function theorem for a class of nonsmooth functions.Math. Oper. Res. 16 (1991), 292-309. Zbl 0746.46039, MR 1106803 |
| Reference:
|
[18] R. T. Rockafellar: On the maximality of sums of nonlinear monotone operators.Trans. Amer. Math. Soc. 149 (1970), 75-88. Zbl 0222.47017, MR 0282272 |
| . |
