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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differentiable selection of optimal solutions in parametric linear programming
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by Dinh The Luc and Pham Huy Dien PDF
Proc. Amer. Math. Soc. 125 (1997), 883-892 Request permission

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.
References
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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
  • 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 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 883-892
  • MSC (1991): Primary 90C31; Secondary 90C05, 49K40
  • DOI: https://doi.org/10.1090/S0002-9939-97-03090-6
  • MathSciNet review: 1301514