This problem generalizes the spectral norm of a matrix (p = q = 2) and the Grothendieck problem (p = ∞, q = 1), and has been widely studied in various regimes. When p ≥ q, the problem exhibits a dichotomy: constant factor approximation algorithms are known if 2 ∈ [q, p], and the problem is hard to approximate within almost polynomial factors when 2 / ∈ [q, p]. The regime when p < q, known as hy...
