Since the 2,1 norm on matrices (1) is separable into the 2 norm of each row, we can treat each row separately.
for simplicity, assume that we have a single row and want to minimize The minimum is either at w = 0 (the tip of the cone) or where the partial derivatives are zero (Figure 3): Clearly, w and v must have the same direction and differ only in magnitude, that is, w = α v v .