一种用于求解等式约束鞍点问题的递归神经网络
A Recurrent Neural Network for Solving Equality-Constrained Saddle Point Problems
摘要: 鞍点问题在工程优化、经济决策、信号处理、智能控制等诸多领域中具有广泛的应用背景，本文针对等式约束下的鞍点问题，提出了一种新型递归神经网络模型。通过构建相应的动力学方程，分析了该神经网络在Lyapunov意义下的稳定性，并证明了其平衡点与原问题最优解的等价性。
Abstract: Saddle point problems have broad applications in various fields such as engineering optimization, economic decision-making, signal processing, and intelligent control. This paper proposes a novel recurrent neural network model for solving equality-constrained saddle point problems. By constructing the corresponding dynamic equations, the stability of the neural network in the Lyapunov sense is analyzed, and the equivalence between its equilibrium point and the optimal solution of the original problem is proven.
文章引用：叶洪志, 李小兵. 一种用于求解等式约束鞍点问题的递归神经网络 [J]. 应用数学进展, 2026, 15(1): 336-350. https://doi.org/10.12677/aam.2026.151033

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