Conditioning, halting criteria and choosing lambda
Abstract. We show the convergence of 1+λ-ES with standard step-size
update-rules on a large family of ﬁtness functions without any convexity
assumption or quasi-convexity assumptions ([3, 6]). The result provides
a rule for choosing λ and shows the consistency of halting criteria based
on thresholds on the step-size.
The family of functions under work is deﬁned through a condition-
number that generalizes usual condition-numbers in a manner that only
depends on level-sets. We consider that the deﬁnition of this condition-
number is the relevant one for evolutionary algorithms; in particular,
global convergence results without convexity or quasi-convexity assump-
tions are proved when this condition-number is ﬁnite.