Theoretical analysis demonstrates equivalence between linear programming and basis pursuit, highlighting shared implications for computational complexity and optimization algorithms.
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)
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Andreas M. Tillmann (2015) studied this question.
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