Lagrange Neural Network for Nonsmooth Nonconvex Optimization Problems with Equality and Inequality Constrains
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摘要: 非凸非光滑优化问题涉及科学与工程应用的诸多领域，是目前国际上的研究热点。该文针对已有基于早期罚函数神经网络解决非光滑优化问题的不足，借鉴Lagrange乘子罚函数的思想提出一种有效解决带等式和不等式约束的非凸非光滑优化问题的递归神经网络模型。由于该网络模型的罚因子是变量，无需计算罚因子的初始值仍能保证神经网络收敛到优化问题的最优解，因此更加便于网络计算。此外，与传统Lagrange方法不同，该网络模型增加了一个等式约束惩罚项，可以提高网络的收敛能力。通过详细的分析证明了该网络模型的轨迹在有限时间内必进入可行域，且最终收敛于关键点集。最后通过数值实验验证了所提出理论的有效性。Abstract: Nonconvex nonsmooth optimization problems are related to many fields of science and engineering applications, which are research hotspots. For the lack of neural network based on early penalty function for nonsmooth optimization problems, a recurrent neural network model is proposed using Lagrange multiplier penalty function to solve the nonconvex nonsmooth optimization problems with equality and inequality constrains. Since the penalty factor in this network model is variable, without calculating initial penalty factor value, the network can still guarantee convergence to the optimal solution, which is more convenient for network computing. Compared with the traditional Lagrange method, the network model adds an equality constraint penalty term, which can improve the convergence ability of the network. Through the detailed analysis, it is proved that the trajectory of the network model can reach the feasible region in finite time and finally converge to the critical point set. In the end, numerical experiments are given to verify the effectiveness of the theoretic results.
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Key words:
- Lagrange neural network /
- Convergence /
- Nonsmooth nonconvex optimization
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