Before revision:  The multilinear framework cannot be directly } applied to the multi-linear extension of a submodular function. We first adapt the continuous greedy algorithm to work for general twice-continuously differentiable functions . The performance of the adapted algorithm depends on a new smoothness parameter. If F: 0,^2 which measures the approximability of the associated problem \max\{F(x):x\in P\}, for solvable downwards-closed polytopes P.
After revision:  The multilinear framework cannot be directly } applied to the 0,^2 which measures the approximability of the associated problem \max\{F(x):x\in P\}, for solvable downwards-closed polytopes P.