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Journal of Convex Analysis 10 (2003), No. 1, 211--227
Copyright Heldermann Verlag 2003
Directional Derivative of a Class of Set-Valued Mappings and its Applications
Zun-Quan Xia
CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China,
zqxiazhh@dlut.edu.cn
Ming-Zheng Wang
CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China
Li-Wei Zhang
CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China
Calculating the directional derivative of a class of the set-valued mappings
G(x) = { z | Az <= 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].
Keywords: Set-valued mapping, directional derivative, perturbed linear programming,
optimal solution set.
MSC 2000: 26D07, 54C60, 58C25, 90C30, 90C31, 90C99.
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