Dt. Luc et Ph. Dien, DIFFERENTIABLE SELECTION OF OPTIMAL-SOLUTIONS IN PARAMETRIC LINEAR-PROGRAMMING, Proceedings of the American Mathematical Society, 125(3), 1997, pp. 883-892
In the present paper we prove that if the data of a parametric linear
optimization problem are smooth, the solution map admits a local smoot
h selection ''almost'' everywhere. This in particular shows that the s
et of points where the marginal function of the problem is nondifferen
tiable is nowhere dense.