| Article ID: | iaor20134154 |
| Volume: | 56 |
| Issue: | 4 |
| Start Page Number: | 1773 |
| End Page Number: | 1790 |
| Publication Date: | Aug 2013 |
| Journal: | Journal of Global Optimization |
| Authors: | Yarotsky Dmitry |
| Keywords: | gaussian processes, global convergence |
We consider the 1D Expected Improvement optimization based on Gaussian processes having spectral densities converging to zero faster than exponentially. We give examples of problems where the optimization trajectory is not dense in the design space. In particular, we prove that for Gaussian kernels there exist smooth objective functions for which the optimization does not converge on the optimum.