A capable neural network model for solving the maximum flow problem.

*(English)*Zbl 1239.90015Summary: We present an optimization technique for solving a maximum flow problem arising in widespread applications in a variety of settings. On the basis of the Karush- Kuhn-Tucker (KKT) optimality conditions, a neural network model is constructed. The equilibrium point of the proposed neural network is then proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the maximum flow problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method.

##### MSC:

90B10 | Deterministic network models in operations research |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

90C20 | Quadratic programming |

37B25 | Stability of topological dynamical systems |

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\textit{A. Nazemi} and \textit{F. Omidi}, J. Comput. Appl. Math. 236, No. 14, 3498--3513 (2012; Zbl 1239.90015)

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