一种新的非线性规划神经网络模型
A Novel Neural Network Model for Nonlinear Programming
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摘要: 提出一种新型的求解非线性规划问题的神经网络模型.该模型由变量神经元、Lagrange 乘子神经元和Kuhn-Tucker乘子神经元相互连接构成.通过将Kuhn-Tucker乘子神经元限 制在单边饱和工作方式,使得在处理非线性规划问题中不等式约束时不需要引入松弛变量,避 免了由于引入松弛变量而造成神经元数目的增加,有利于神经网络的硬件实现和提高神经网 络的收敛速度.可以证明,在适当的条件下,文中提出的神经网络模型的状态轨迹收敛到与非 线性规划问题的最优解相对应的平衡点.Abstract: A novel neural network model for solving nonlinear programming problems is proposed in this paper. It is composed of variable neurons, Lagrange multiplier neurons and Kuhn-Tucker multiplier neurons which are interconnected. By making the Kuhn-Tucker multiplier neurons operate in an one-sided saturated mode, the introduction of the slack variables is no more necessary in dealing with the inequality constraints of nonlinear programming problems. This method can avoid the increase in the number of neurons caused by the slack variables. This is advantageous to the hardware implementation and the convergence rate improvement. It can be shown that under suitable conditions the trajectory of the proposed neural network model converges to the equilibrium point corresponding to the optimal solution of the nonlinear programming problem.
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Key words:
- Neural network /
- nonlinear programming /
- optimization
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