On the Second-Order Contingent Set and Differential Inclusions

Brahim Aghezzaf; Saïd Sajid

doi:10.68381/jca07009

Abstract

It is shown that the second-order contingent set to a closed convex set coincides with the contingent cone to this set. Furthermore, sufficient conditions are given to prove the existence of viable solution for second-order differential inclusions.

Author information

Contact details are reproduced from the original publication and may be historical.

Brahim Aghezzaf

Dép. de Mathématiques, Faculté des Sciences, 5366 Maarif, Casablanca, Maroc

Saïd Sajid

Dép. de Mathématiques, F. S. T. M., Mohammadia, Maroc

Keywords

Continuous multifunctions
compact multifunctions
contingent cone
second-order contingent set

Mathematics Subject Classification

34A60

References

J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhauser, 1990.Google Scholar
A. Auslender. R. Cominitti: A comparative study of multifunction differentiability with applications in mathematical programming, MOR 16(2) (1991) 240-258.https://doi.org/10.1287/moor.16.2.240 Google Scholar
A. Auslender, J. Mechler: Second Order Viability Problems for Differential Inclusions, Academic Press Inc., 1994.https://doi.org/10.1006/jmaa.1994.1015 Google Scholar
A. Ben-Tal: Second order theory of extremum problems, in: Extremal Methods and System Analysis, Lecture Notes in Economics and Mathematical Systems 174, (A. V. Fiacco, Kortanek, eds.), Springer-Verlag, New-York, 1980, 336-356.https://doi.org/10.1007/978-3-642-46414-0_16 Google Scholar
B. Cornet, G. Haddad: Théorème de viabilité pour les inclusions différentielles du second ordre, Isr. J. Math. 57(2) (1987) 225-238.https://doi.org/10.1007/BF02772175 Google Scholar
G. Haddad: Monotone trajectories of differential inclusions and functional differential inclusions with memory, Isr. J. Math. 39 (1981) 83-100.https://doi.org/10.1007/BF02762855 Google Scholar
H. Kawasaki: Second order necessary conditions of the Kuhn-Tucker type under new constraint qualifications, J. Optmization Theory Applications 57(2) (1988).https://doi.org/10.1007/BF00938539 Google Scholar
R. T. Rockafellar: Pseudo-differentiability of set-valued mappings and its applications in optimization, in: Analyse non Linéaire, H. Attouch, Gautier-Villars (1989) 449-482.https://doi.org/10.1016/s0294-1449(17)30034-3 Google Scholar

Suggested citation

Published by Heldermann Verlag, 2000. Rights now held by Banach Press LLC.

[1] J. P. Aubin, H. Frankowska: Set-Valued Analysis, Birkhauser, 1990.Google Scholar

[2] A. Auslender. R. Cominitti: A comparative study of multifunction differentiability with applications in mathematical programming, MOR 16(2) (1991) 240-258.https://doi.org/10.1287/moor.16.2.240 Google Scholar

[3] A. Auslender, J. Mechler: Second Order Viability Problems for Differential Inclusions, Academic Press Inc., 1994.https://doi.org/10.1006/jmaa.1994.1015 Google Scholar

[4] A. Ben-Tal: Second order theory of extremum problems, in: Extremal Methods and System Analysis, Lecture Notes in Economics and Mathematical Systems 174, (A. V. Fiacco, Kortanek, eds.), Springer-Verlag, New-York, 1980, 336-356.https://doi.org/10.1007/978-3-642-46414-0_16 Google Scholar

[5] B. Cornet, G. Haddad: Théorème de viabilité pour les inclusions différentielles du second ordre, Isr. J. Math. 57(2) (1987) 225-238.https://doi.org/10.1007/BF02772175 Google Scholar

[6] G. Haddad: Monotone trajectories of differential inclusions and functional differential inclusions with memory, Isr. J. Math. 39 (1981) 83-100.https://doi.org/10.1007/BF02762855 Google Scholar

[7] H. Kawasaki: Second order necessary conditions of the Kuhn-Tucker type under new constraint qualifications, J. Optmization Theory Applications 57(2) (1988).https://doi.org/10.1007/BF00938539 Google Scholar

[8] R. T. Rockafellar: Pseudo-differentiability of set-valued mappings and its applications in optimization, in: Analyse non Linéaire, H. Attouch, Gautier-Villars (1989) 449-482.https://doi.org/10.1016/s0294-1449(17)30034-3 Google Scholar