 Relative-entropy Lyapunov function for resource prices

For a complementary-slackness optimum ${\mu }^{\ast }$, defineinterpreting a zero-reference summand as ${\mu }_j/{\kappa }_j$. This is a nonnegative generalized reverse-relative-entropy expression for positive resource prices. Along multiplicative resource-price dynamics, with $p=A^T\mu$ and $g=Ax-C$,Its sublevel bounds keep all route prices away from zero and permit the LaSalle invariance principle, including optima with some zero individual prices.