.We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved in polynomial time in certain situations, and we discuss how it can be approximated in other cases. Along the way, we investigate the concept of push-forward and pull-back of seminorms, which leads us to uncover novel duality principles that come into play when optimizing over the unit ball of norms.Reproducibility of computational results.This paper has been awarded the "SIAM Reproducibility Badge: Code and data available" as a recognition that the authors have followed reproducibility principles valued by SIMAX and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://codeocean.com/capsule/8982170/tree and in the supplementary materials (RBcode.zip 43.0MB).Keywordsoperator normpush-forward normpull-back normapproximationMSC codes15A6065F3568Q25
Adrian Kulmburg (Wed,) studied this question.