Equivalence of Linear Programming and Basis Pursuit

Abstract

In this note, we show that linear programming and the prominent Basis Pursuit problem (i.e., minimizing the ℓ 1 ‐norm of a vector x subject to an underdetermined linear equation system Ax  =  b ) are theoretically equivalent, and briefly discuss possible ramifications regarding computational complexity and practical applicability. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)