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subject to −y x y −1 Ax−b 1 with variables x ∈ Rn and y ∈ Rn. Another reformulation is to write x as the diﬀerence of two nonnegative vectors x = x+ −x−, and to express the problem as minimize 1Tx+ +1Tx− subject to −1 Ax+ −Ax− −b 1 x+ 0, x− 0, with variables x+ ∈ Rn and x− ∈ Rn. (e) Equivalent to minimize 1Ty +t subject to −y Ax−b y −t1 x t1, with

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