Editing Random optimization (section)

== Convergence and variants ==
Matyas showed the basic form of RO converges to the optimum of a simple [[unimodal function]] by using a [[Limit (mathematics)|limit-proof]] which shows convergence to the optimum is certain to occur if a potentially infinite number of iterations are performed. However, this proof is not useful in practice because a finite number of iterations can only be executed. In fact, such a theoretical limit-proof will also show that purely random sampling of the search-space will inevitably yield a sample arbitrarily close to the optimum.

Mathematical analyses are also conducted by Baba <ref name=baba81convergence/> and Solis and Wets <ref name=solis81random/> to establish that convergence to a region surrounding the optimum is inevitable under some mild conditions for RO variants using other [[probability distribution]]s for the sampling. An estimate on the number of iterations required to approach the optimum is derived by Dorea.<ref name=dorea83expected/> These analyses are criticized through empirical experiments by Sarma <ref name=sarma90convergence/> who used the optimizer variants of Baba and Dorea on two real-world problems, showing the optimum to be approached very slowly and moreover that the methods were actually unable to locate a solution of adequate fitness, unless the process was started sufficiently close to the optimum to begin with.