## 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