On the properties of optimal point configurations for a family of comparison functionals for metric configurations

The problem of searching for an optimal point configuration (i.e., a set of points such that the distances between them best fit a given metric configuration) is considered. An upper bound is obtained for the dimension of a space in which any metric configuration can be represented exactly or approximately by an optimal point configuration. It is shown that, if there is no point configuration that exactly represents a given metric configuration, then, for a natural family of comparison functionals for metric configurations, the dimension of a space in which there is an optimal point configuration is lower than the dimension required in the general case for representing a metric configuration of a given cardinality.