DOI: 10.68381/jca1011 ISSN: 0944-6532
Directional Derivative of a Class of Set-Valued Mappings and its Application
Zun-Quan Xia, Ming-Zheng Wang, Li-Wei Zhang
Calculating the directional derivative of a class of the set-valued mappings
G(x) = \{z \mid Az \leq h(x)\}
G
(
x
)
=
{
z
∣
A
z
≤
h
(
x
)
}
, in the sense of Y. N. Tyurin [Econ. Math. Methods 1 (1965) 391–410] and H. T. Banks and M. Q. Jacobs [J. Math. Anal. Appl. 29 (1970) 246–272] is presented that can be viewed as an extension to the one given by Pecherskaya. Results obtained in this paper are used to get a bound of the Lipschitz constant for the solution sets of Perturbed Linear Programming. This new bound is smaller than the one due to W. Li [SIAM J. Control Optimizaton 32 (1994) 140–153].