
Journal of Convex Analysis 10 (2003), No. 1, 211227 Copyright Heldermann Verlag 2003 Directional Derivative of a Class of SetValued Mappings and its Applications ZunQuan Xia CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China, zqxiazhh@dlut.edu.cn MingZheng Wang CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China LiWei Zhang CORA, Dept. of Applied Mathematics, University of Technology, Dalian 116024, China Calculating the directional derivative of a class of the setvalued mappings G(x) = { z  Az <= h(x) }, in the sense of Y. N. Tyurin [Econ. Math. Methods 1 (1965) 391410] and H. T. Banks and M. Q. Jacobs [J. Math. Anal. Appl. 29 (1970) 246272] 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) 140153]. Keywords: Setvalued mapping, directional derivative, perturbed linear programming, optimal solution set. MSC 2000: 26D07, 54C60, 58C25, 90C30, 90C31, 90C99. FullTextpdf (492 K) 