 Note that a generalized capability of evolution strategies to adapt a covariance matrix reflective of the inverse-Hessian has been proven for a static model relying on a quadratic approximation.The update equations for mean and covariance matrix maximize a likelihood while resembling an expectation-maximization algorithm.The update of the mean vector formula_7 maximizes a log-likelihood, such that

where

denotes the log-likelihood of formula_1 from a multivariate normal distribution with mean formula_7 and any positive definite covariance matrix formula_31.