  The class of algorithms called Hessian Estimation Evolution Strategies
(HE-ESs) update the covariance matrix of their sampling distribution by
directly estimating the curvature of the objective function. The approach is
practically efficient, as attested by respectable performance on the BBOB
testbed, even on rather irregular functions.
  In this paper we formally prove two strong guarantees for the (1+4)-HE-ES, a
minimal elitist member of the family: stability of the covariance matrix
update, and as a consequence, linear convergence on all convex quadratic
problems at a rate that is independent of the problem instance.
