  The subject of this paper is regularity-preserving aggregation of regular
norms on finite-dimensional linear spaces. Regular norms were introduced in [5]
and are closely related to ``type 2'' spaces [9, Chapter 9] playing important
role in 1) high-dimensional convex geometry and probability in Banach spaces
[0.9.12.13.15], and in 2) design of proximal first-order algorithms for
large-scale convex optimization with dimension-independent, or nearly so,
complexity. Regularity, with moderate parameters, of a norm makes applicable,
in a dimension-independent fashion, numerous geometric, probabilistic, and
optimization-related results, which motivates our interest in aggregating
regular norms with controlled (and moderate) inflation of regularity
parameters.
