Convergence of the Non-Uniform Physarum Dynamics

@article{Karrenbauer2020ConvergenceOT,
  title={Convergence of the Non-Uniform Physarum Dynamics},
  author={A. Karrenbauer and P. Kolev and K. Mehlhorn},
  journal={ArXiv},
  year={2020},
  volume={abs/1901.07231}
}
  • A. Karrenbauer, P. Kolev, K. Mehlhorn
  • Published 2020
  • Physics, Computer Science
  • ArXiv
  • Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in \mathbb{Z}^n$. We show under fairly general conditions that the non-uniform Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right) \] converges to the optimum solution $x^*$ of the weighted basis pursuit problem minimize $c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to the constraints $A q = b$ and… CONTINUE READING
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