  Several recent publications investigated Markov-chain modelling of linear
optimization by a $(1,\lambda)$-ES, considering both unconstrained and linearly
constrained optimization, and both constant and varying step size. All of them
assume normality of the involved random steps, and while this is consistent
with a black-box scenario, information on the function to be optimized (e.g.
separability) may be exploited by the use of another distribution. The
objective of our contribution is to complement previous studies realized with
normal steps, and to give sufficient conditions on the distribution of the
random steps for the success of a constant step-size $(1,\lambda)$-ES on the
simple problem of a linear function with a linear constraint. The decomposition
of a multidimensional distribution into its marginals and the copula combining
them is applied to the new distributional assumptions, particular attention
being paid to distributions with Archimedean copulas.
