IEEE Trans Neural Netw Learn Syst. 2014 Apr;25(4):824-30. doi: 10.1109/TNNLS.2013.2280905.
In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.
在这篇简短的文章中，基于罚函数方法，提出了一种通过微分包含来建模的递归神经网络（NN），用于求解双层线性规划问题（BLPP）。与现有的 BLPP 的 NN 相比，该模型具有最少的状态变量和简单的结构。使用非光滑分析、微分包含理论和 Lyapunov 类方法，在一定条件下，所提出的神经网络的平衡点序列可以近似收敛到 BLPP 的最优解。最后，供应链分配模型的数值模拟表明，所提出的递归神经网络具有优异的性能。
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