Pınar, Mustafa Ç.2020-02-102020-02-1020190895-4798http://hdl.handle.net/11693/53208The problem of exact recovery of an individual sparse vector using the Basis Pursuit (BP) model is considered. A differentiable Huber loss function (a convex quadratic spline) is used to replace the $\ell_1$-norm in the BP model. Using the theory of duality and classical results from quadratic perturbation of linear programs, a necessary condition for exact recovery leading to a negative result is given. An easily verifiable sufficient condition is also presented.EnglishExact recovery of a sparse vectorBasis pursuitHuber loss functionStrictly convex quadratic programmingLinear programmingConvex quadratic splinesℓ1-normQuadratic perturbationArticle10.1137/18M1185375