An implicit-function theorem for a class of monotone generalized equations

Walter Alt; Iosif Kolumbán

Kybernetika (1993)

  • Volume: 29, Issue: 3, page 210-221
  • ISSN: 0023-5954

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Alt, Walter, and Kolumbán, Iosif. "An implicit-function theorem for a class of monotone generalized equations." Kybernetika 29.3 (1993): 210-221. <http://eudml.org/doc/28261>.

@article{Alt1993,
author = {Alt, Walter, Kolumbán, Iosif},
journal = {Kybernetika},
keywords = {implicit function theorem; generalized equations; monotone set-valued mapping; Hilbert spaces; nonsmooth functions},
language = {eng},
number = {3},
pages = {210-221},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An implicit-function theorem for a class of monotone generalized equations},
url = {http://eudml.org/doc/28261},
volume = {29},
year = {1993},
}

TY - JOUR
AU - Alt, Walter
AU - Kolumbán, Iosif
TI - An implicit-function theorem for a class of monotone generalized equations
JO - Kybernetika
PY - 1993
PB - Institute of Information Theory and Automation AS CR
VL - 29
IS - 3
SP - 210
EP - 221
LA - eng
KW - implicit function theorem; generalized equations; monotone set-valued mapping; Hilbert spaces; nonsmooth functions
UR - http://eudml.org/doc/28261
ER -

References

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  2. W. Alt, Parametric programming with applications to optimal control and sequential quadratic programming, Bayreuther Mathematische Schriften 35 (1991), 1-37. (1991) MR1104518
  3. J.-P. Aubin, I. Ekeland, Applied Nonlinear Analysis, J. Wiley, New York 1984. (1984) Zbl0641.47066MR0749753
  4. J.-P. Aubin, H. Frankowska, Set-valued Analysis, Birkhauser, Boston 1990. (1990) Zbl0713.49021MR1048347
  5. F. E. Browder, Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces, Amer. Math. Soc, Providence, Rhode Island 1976. (1976) Zbl0327.47022MR0405188
  6. S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. IS (1988), 421-434. (1988) Zbl0674.49007MR0961802
  7. A. V. Fiacco, Sensitivity analysis for nonlinear programming using penalty methods, Math. Programming 10 (1976), 287-311. (1976) Zbl0357.90064MR0434444
  8. A. V. Fiacco, Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Academic Press, New York - London 1983. (1983) Zbl0543.90075MR0721641
  9. A. D. Ioffe, V. M. Tihomirov, Theory of Extremal Problems, North-Holland, Amsterdam - New York - Oxford 1979. (1979) Zbl0407.90051MR0528295
  10. K. Ito, K. Kunisch, Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimation, Preprint, 1989. (1989) MR1178394
  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. (1988) Zbl0664.46045MR0989594
  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. (1989) Zbl0724.47027MR1043190
  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). Zbl0756.90093MR1133252
  14. G. Minty, Monotone (nonlinear) operators in Hilbert spaces, Duke Math. J. 29 (1962), 341-346. (1962) MR0169064
  15. S. M. Robinson, Strongly regular generalized equations, Math. Oper. Res. 5 (1980), 43-62. (1980) Zbl0437.90094MR0561153
  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. (1983) Zbl0554.34007MR0717407
  17. S. M. Robinson, An implicit-function theorem for a class of nonsmooth functions, Math. Oper. Res. 16 (1991), 292-309. (1991) Zbl0746.46039MR1106803
  18. R. T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75-88. (1970) Zbl0222.47017MR0282272

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