Linear regression estimators for multinormal distributions in optimization of stochastic programming problems

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.