Differentiable selection of optimal solutions in parametric linear programming

Luc, Dinh; Pham Huy Dien

doi:10.1090/S0002-9939-97-03090-6

Differentiable selection of optimal solutions in parametric linear programming
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by Dinh The Luc and Pham Huy Dien

Proc. Amer. Math. Soc. 125 (1997), 883-892

DOI: https://doi.org/10.1090/S0002-9939-97-03090-6

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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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