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Differentiable selection of optimal solutions in parametric linear programming

Author(s): Dinh The Luc; Pham Huy Dien
Journal: Proc. Amer. Math. Soc. 125 (1997), 883-892.
MSC (1991): Primary 90C31; Secondary 90C05, 49K40
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Abstract: In the present paper we prove that if the data of a parametric linear optimization problem are smooth, the solution map admits a local smooth selection ``almost'' everywhere. This in particular shows that the set of points where the marginal function of the problem is nondifferentiable is nowhere dense.

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Additional Information:

Dinh The Luc
Affiliation: Institute of Mathematics, P.O. Box 10000 Boho, Hanoi, Vietnam

Pham Huy Dien
Affiliation: Institute of Mathematics, P.O. Box 10000 Boho, Hanoi, Vietnam

DOI: 10.1090/S0002-9939-97-03090-6
PII: S 0002-9939(97)03090-6
Received by editor(s): March 28, 1994
Received by editor(s) in revised form: September 13, 1994
Additional Notes: This work was supported in part by the Program on Applied Mathematics and was completed during the authors' stay at the Laboratory for Applied Mathematics, University of Pau, France
Communicated by: Joseph S. B. Mitchell
Copyright of article: Copyright 1997, American Mathematical Society


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