Abstract
For a bounded system of linear equalities and inequalities, we show that the NP-hard ℓ 0-norm minimization problem is completely equivalent to the concave ℓ p -norm minimization problem, for a sufficiently small p. A local solution to the latter problem can be easily obtained by solving a provably finite number of linear programs. Computational results frequently leading to a global solution of the ℓ 0-minimization problem and often producing sparser solutions than the corresponding ℓ 1-solution are given. A similar approach applies to finding minimal ℓ 0-solutions of linear programs.
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