一种解决半定规划问题的投影神经网络方法
A Projection Neural Network Method for Solving Semidefinite Programming Problems
摘要: 本文研究了半定规划(SDP)问题的神经网络方法。首先提出了一种基于投影算子的神经网络方法，然后，建立了神经网络平衡点与半定规划问题最优解之间的等价性，并证明了平衡点具有Lyapunov稳定性。数值模拟进一步证明了该网络的有效性。通过利用投影映射和SDP问题的结构，该神经网络方法可以有效地解决优化任务，为解决各种半定规划问题提供了一个实用的计算框架。
Abstract: This paper studies the neural network method for semidefinite programming (SDP) problems. Firstly, a neural network method based on projection operator is proposed. Then, the equivalence between the equilibrium point of the neural network and the optimal solution of the semidefinite programming problem is established, and it is proved that the equilibrium point has Lyapunov stability. Numerical simulation further proves the effectiveness of the network. By using the structure of projection mapping and SDP problem, the neural network method can effectively solve the optimization task, and provides a practical computational framework for solving various semidefinite programming problems.
文章引用：张柯冕, 张杰, 杨嘉妮. 一种解决半定规划问题的投影神经网络方法[J]. 计算机科学与应用, 2025, 15(10): 232-239. https://doi.org/10.12677/csa.2025.1510263

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