Figure 2
From: Partial inhibition and bilevel optimization in flux balance analysis
Convexity of L1- and L2-formulations and uniqueness of the solution. The two pictures report the unperturbed fluxes (vut) in the original set W. When the inhibition h is applied (dotted blue line), the set reduces to W(h). (a) With the L1-norm, balls are not strictly convex, therefore cases of multiple equivalent solutions may appear. As one can see, these situations occur only when the hyperplane of W(h) which realizes the minimum distance with respect to vut is parallel to an edge of the L1-ball. (b) Conversely, L2 balls are strictly convex and always lead to a unique solution.