Convergence properties of the expected improvement algorithm with fixed mean and covariance functions

This paper deals with the convergence of the expected improvement algorithm, a popular global optimization algorithm based on a Gaussian process model of the function to be optimized. The first result is that under some mild hypotheses on the covariance function k of the Gaussian process, the expected improvement algorithm produces a dense sequence of evaluation points in the search domain, when the function to be optimized is in the reproducing kernel Hilbert space generated by k  . The second result states that the density property also holds for P-almostP-almost all continuous functions, where P is the (prior) probability distribution induced by the Gaussian process.