基于精确罚函数的一类广义非线性神经网络模型

A General Model of Non-Linear Neural Networks Based on Exact Penalty Function

针对一般的非线性优化问题定义了一种 2次非线性罚函数 ,证明了在一定条件下对应的罚优化问题的精确罚定理 ,由此引进了一种广义非线性神经网络模型 ,并证明了这种网络的平衡点与能量函数之间的联系 ,在一定条件下对应的平衡点收敛到原问题的最优解 .这种神经网络模型对于求解许多优化问题具有重要的作用 .

A double non-linear penalty function is defined for the non-linear optimality problems (NP) and the exact penalty theorem is exacted under some conditions. A new general model of non-linear neural networks is introduced and the relationship between the equilibrium points and the energy function is showed. Under the given condition, the equilibrium point of the neural networks converges to a solution of NP. This model plays an important part in many optimal problems.