Equivalence of Minimal ℓ 0- and ℓ p -Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p

G. M. Fung and O. L. Mangasarian ()
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G. M. Fung: Siemens Medical Solutions, Inc.
O. L. Mangasarian: University of Wisconsin

Journal of Optimization Theory and Applications, 2011, vol. 151, issue 1, No 1, 10 pages

Abstract: 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.

Keywords: ℓ0-minimization; Linear equations; Linear inequalities; Linear programming (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10957-011-9871-x

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