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

  • G. M. Fung
  • O. L. MangasarianEmail author


For a bounded system of linear equalities and inequalities, we show that the NP-hard 0-norm minimization problem is completely equivalent to the concave 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 0-minimization problem and often producing sparser solutions than the corresponding 1-solution are given. A similar approach applies to finding minimal 0-solutions of linear programs.


0-minimization Linear equations Linear inequalities Linear programming 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.R&D Clinical SystemsSiemens Medical Solutions, Inc.MalvernUSA
  2. 2.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA
  3. 3.Mathematics DepartmentUniversity of California at San DiegoLa JollaUSA

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