components in this casethe mean vector and the vector of variances are simply updated via the sample mean and sample variance of the elite samples this is known as normal updating generic ce procedure for minimization is given in algorithm normal updating algorithm cross-entropy method for minimization inputfunction initial sampling parameter sample size nrarity parameter %smoothing parameter outputapproximate minimum of and optimal sampling parameter elite initialize set %ne and while stopping criterion is not met do - + simulate an iid sample from the density (vt- evaluate the performances ( ) ( and sort them from smallest to largests ( ( let gt be the sample %-quantile of the performancesgt ( elite ( determine the set of elite samples et {xi (xi gt let be the mle of the elite samplesx argmax ln ( vv ( xet update the sampling parameter as vt av ( )vt- ( return gt vt the ce algorithm produces sequence of pairs ( )( )such that gt converges (approximatelyto the minimal function valueand (vt to degenerate pdf that (approximatelyconcentrates all its mass at minimizer of as possible stopping condition is to stop when the sampling distribution (vt is sufficiently close to degenerate distribution for normal updating this means that the standard deviation is sufficiently small the output of the ce algorithm could also include the overall best function value and corresponding solution in the following examplewe minimize the same function as in example but instead use the ce algorithm example (cross-entropy method for minimizationin this case we take the family of normal distributions { (us )for the sampling step (step of algorithm )starting with and the choice of the initial parameter is quite arbitraryas long as is large enough to sample wide range of points we take samples at each iterationset and keep the elite dn% smallest ones as the elite samples the parameters and are then updated via the sample mean and sample standard deviation