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By exploiting some properties of the<jats:italic>k<\/jats:italic>-norm of a vector, namely, of the sum of its<jats:italic>k<\/jats:italic>largest absolute-value components, we formulate a sparse optimization problem as a mixed-integer nonlinear program, whose continuous relaxation is equivalent to the unconstrained minimization of a difference-of-convex function. The approach is applied to Feature Selection in the support vector machine framework, and tested on a set of benchmark instances. 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