| 摘要: |
| 针对神经网络应用于解决线性和非线性约束下的复数优化问题，提出了一种简化的复数神经网络解决非线性规划下的拟凸优化问题；通过定义辅助函数将复数域上的拟凸优化问题转化为实数域上的优化问题，推导出相应的神经网络模型，并建立李雅普诺夫函数证明该神经网络平衡解的稳定性与收敛性；得出对任意的初始点，该神经网络是李雅普诺夫全局稳定的而且收敛于优化问题的最优解；通过数值算例验证了此研究方法的有效性以及结论的正确性。 |
| 关键词: 复数神经网络，拟凸优化，李雅普诺夫函数 |
| DOI： |
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| The Solution to Quasi convex Optimization Problems Based on Recurrent Neural Network |
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LI Jing
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| Abstract: |
| According to application of neural network to solving recurrent optimization problems under linear and nonlinear constraints，this paper proposes a simplified recurrent neural network for solving quasi convex optimization problems under nonlinear programming.The quasi convex optimization problems on complex domain are transformed into the optimization problems on real number domain by defining auxiliary function，the corresponding neural network model is derived，and the stability and convergence of the equilibrium solution of this neural network is proved by established Lyapunov function.For arbitrary initial point，this neural network is Lyapunov global stable and the optimal solution converging at optimization problem.Numerical example verifies the validity of this method and the correctness of the conclusion. |
| Key words: recurrent neural network quasi convex optimization Lyapunov function |
