Dual congestion potential
= Dual congestion potential
{title2=$H(\mu)=\sum_j\int_0^{\mu_j}q_j(u)\,du-\sum_rw_r\log(A^T\mu)_r$}
For strictly increasing continuous supply functions $q_j$ with $q_j(0)=0$, this potential is strictly convex on prices with positive route-price sums. Its minimum is interior for every used resource and gives the unique positive-price equilibrium. Multiplicative price dynamics can also have <boundary equilibria of multiplicative price dynamics> if zero prices are permitted.