A New One-layer Recurrent Neural Network for Solving Nonsmooth Pseudoconvex Optimization Problems
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摘要: 非光滑伪凸优化问题是一类比较特殊的非凸优化问题，常出现在各类科学与工程应用中，因此具有很大的研究价值。针对现有神经网络模型解决非光滑伪凸优化问题存在的不足，该文基于微分包含理论，提出一种新型单层递归神经网络模型。通过理论分析，证明了神经网络状态解在有限时间内收敛到可行域，且永驻其中，最终神经网络状态解收敛于原优化问题的最优解。最后，通过数值实验，验证了所提理论的有效性。与现有的神经网络相比，该文所提神经网络模型结构简单仅为单层，不需要提前计算罚参数，且对初始点选取没有任何特殊的要求。Abstract: Pseudoconvex optimization problems are a special kind of nonconvex optimization problems, which often appear in various scientific and engineering applications, so they have great research value. Considering the shortcomings of the existing neural network model to solve the nonsmooth pseudoconvex optimization problem, a new single-layer recurrent neural network model based on differential inclusion theory is proposed. Through theoretical analysis, it is proved that the state solution of the neural network converges to the feasible region within a limited time and stays in it forever. Finally, the state solution of the neural network converges to the optimal solution of the original optimization problem. At the end of the article, the validity of the proposed theory is verified through numerical experiments. Compared with existing neural networks, the neural network model proposed in this paper is simple in structure, does not need to calculate penalty parameters in advance, and has no special requirements for the selection of initial points.
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Key words:
- Neural network /
- Nonsmooth pseudoconvex optimization /
- Convergence /
- Optimal solution
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