An L<sub>1</sub> Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems

LI Hai-bin; DUAN Zhi-xin

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An L₁ Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems

更新时间：2025-07-16

- An L₁ Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems
- Acta Electronica Sinica Vol. 37, Issue 1, Pages: 229-234(2009)
- 作者机构：
  
  内蒙古工业大学理学院,内蒙古,呼和浩特,010051
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP183
- Published：2009
- 稿件说明：
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LI Hai-bin, DUAN Zhi-xin. An L₁ Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems[J]. Acta Electronica Sinica, 2009, 37(1): 229-234.
DOI：

LI Hai-bin, DUAN Zhi-xin. An L₁ Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems[J]. Acta Electronica Sinica, 2009, 37(1): 229-234. DOI：

摘要

优化计算是神经网络的一个重要应用领域.针对已有神经网络求解约束非线性规划问题时

不能兼顾网络规模、计算效率、精确性的问题

本文提出了一种基于精确罚函数的约束非线性规划问题的神经网络计算方法.将约束非线性规划问题的一种

精确罚函数作为神经网络的能量函数

利用该能量函数的最速下降原理构造了神经网络的动力学方程并给出了其稳定收敛性说明.理论分析及算例仿真表明

所提出神经网络动力学方程能够全局、精确收敛于原规划问题的一个局部最优解.特别是

该神经网络动力学方程易于映射为动态电路

是一种工程优化问题的实时计算方法.

Abstract

Optimization calculation is one of the important application fields in Neural Network.This paper proposes a Neural Network computational method of nonlinear programming problems based on precise F-function for the problems of not catering to network size

computational efficiency and accuracy when solving the constraint nonlinear programming problems in current Neural Network.A low order precise F-function of constraint nonlinear programming problems is served as energy function of Neural Network.The dynamics equation of Neural Network is constructed and the clarification of its stability is given by the most rapid decreasing principle of the energy function.Theoretical analysis and computational example emulation show that the proposed Neural Network dynamics equation globally and precisely constringes a local optimization solution of the original programming problems.In particular

the neural network dynamics equation is easy to be mapped as dynamic circuit

which is a Real-time calculation method for engineering optimization problems.

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Department of Automatic Control,Beijing Institute of Technology

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An L1 Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems

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An L₁ Exact Penalty Function Neural Network Method for Constraint Nonlinear Programming Problems