Semidefinite programs for completely bounded norms

TL;DR

This paper demonstrates that completely bounded trace and spectral norms can be computed and verified efficiently using semidefinite programming, offering new proofs and computational methods for these mathematical norms.

Contribution

The paper introduces semidefinite programming formulations for completely bounded norms, enabling efficient calculation and verification, and provides alternative proofs for known properties.

Findings

Complete characterization of norms via semidefinite programs

Efficient computational methods for these norms

Alternative proofs of known properties

Abstract

The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them.