Lagrange-Type Neural Networks for Nonlinear Programming Problems with Inequality Constraints

2006 ◽  
Author(s):  
Yuancan Huang
Keyword(s):  
Neural Networks ◽  
Nonlinear Programming ◽  
Inequality Constraints

IMPROVED NEURAL NETWORKS FOR LINEAR AND NONLINEAR PROGRAMMING

1991 ◽  
Vol 02 (04) ◽  
pp. 331-339 ◽  
Author(s):  
Jiahan Chen ◽  
Michael A. Shanblatt ◽  
Chia-Yiu Maa
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Nonlinear Programming ◽  
Penalty Function ◽  
New Combination ◽  
Optimal Point ◽  
Linear And Nonlinear Programming ◽  
Linear And Nonlinear ◽  
Simulation Results

A method for improving the performance of artificial neural networks for linear and nonlinear programming is presented. By analyzing the behavior of the conventional penalty function, the reason for the inherent degenerating accuracy is discovered. Based on this, a new combination penalty function is proposed which can ensure that the equilibrium point is acceptably close to the optimal point. A known neural network model has been modified by using the new penalty function and the corresponding circuit scheme is given. Simulation results show that the relative error for linear and nonlinear programming is substantially reduced by the new method.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

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