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Linear regression estimators for multinormal distributions in optimization of stochastic programming problems. (English) Zbl 0937.90074

Summary: Several linear regression estimators are presented, which approximate the distribution function of the \(m\)-dimensional normal distribution, or the distribution function along a line. These regression estimators are quadratic functions, or simple functions of quadratic functions and can be applied in numerical problems, arising during optimization of stochastic programming problems. A root finding procedure is developed, that can be used to find the intersection of a line and the border of the feasible set. Directional derivatives and gradient of the normal distribution can be computed. Some numerical results are also presented.

MSC:

90C15 Stochastic programming
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