pycvxset: A Python package for convex set manipulation

The paper explicitly claims that Y ⊆ X if and only if the optimal value of program (12) is nonnegative, for the objective minimize 1 + α^T(c_Y − G_X ξ_X − c_X) − β^T b_{e,Y} subject to ||ξ_X||_∞ ≤ 1, A_{e,X} ξ_X = b_{e,X}, and ||G_Y^T α + A_{e,Y}^T β||_1 ≤ 1 (decision variables α, β, ξ_X) . A careful duality/support-function analysis shows the opposite: the program is nonnegative if and only if X ⊆ Y. A 1D counterexample (X = [−1,1], Y = [−1/2,1/2]) gives an optimal value of −1 even though Y ⊆ X holds, directly falsifying the paper’s equivalence. Hence the inclusion direction in the paper is reversed.