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On the smoothness of an objective function in quantile optimization problems. (English. Russian original) Zbl 0920.90109
Autom. Remote Control 58, No. 9, Pt. 1, 1459-1468 (1997); translation from Avtom. Telemekh. 1997, No. 9, 69-80 (1997).
Summary: The paper is concerned with the issue of differentiability of the quantile function, the criterion that is commonly used in stochastic optimization problems. Two cases are studied: when the quantile function can be represented as an implicit function using the probability function, and when the quantile function can be approximated by the maximum function over some confidence set. In the second case, the quantile function turns out to be differentiable, which is not always the case for the probability function.

90C15 Stochastic programming