Abstract

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].

Author information

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

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

Keywords

  • Set-valued mapping
  • directional derivative
  • perturbed linear programming
  • optimal solution set

Mathematics Subject Classification

26D07, 54C60, 58C25, 90C30, 90C31, 90C99

Suggested citation

Z.-Q. Xia, M.-Z. Wang, L.-W. Zhang. “Directional Derivative of a Class of Set-Valued Mappings and its Applications.” Journal of Convex Analysis 10 (2003), No. 1, 211–227.

Copyright Heldermann Verlag 2003