Convergence of the Non-Uniform Physarum Dynamics

Let $c mathbb{Z}^m_{u003e 0}$, $A mathbb{Z}^{ntimes m}$, and $b mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics [ dot{x}_e = a_e(x,t) left(|q_e| - x_eright) ] converges to the optimum solution $x^*$ of the weighted basis pursuit problem minimize $c^T x$ subject to $A f = b$ and $|f| le x$. H...More