A new measure of irregularity of distribution and quasi-Monte Carlo methods for global optimization

摘要: Measures of irregularity distribution, such as discrepancy and dispersion, play a major role in quasi-Monte Carlo methods for integration optimization. In this paper, new measure called volume-dispersion, is introduced. Its relation to the traditional its applications global optimization problems are investigated. Optimization errors bounded terms volume-dispersion. Also, volume-dispersion generalized so-called F-volume-dispersion quasi-F-volume-dispersion. They reasonable measures representation point sets given probability distributions on general domains have potential when prior knowledge about possible location optimizer known experimental designs. Methods generating with low quasi-F-volume-dispersion described.