In this comment we briefly explain that the change in the BPCG algorithm in the FrankWolfe.jl package does not adverse affect convergence (up to a very small constant factor), while improving sparsity. Starting point is Lemma 3.5 in the original BPCG paper. The algorithm now uses the new condition: $$ \tag{relaxCond} K \cdot \langle \nabla f(x_t), a_t - s_t \rangle \geq \langle \nabla f(x_t), x_t - w_t \rangle, $$