Another Simple Recurrent Neural Network for Quadratic and Linear Programming

A new recurrent neural network is proposed for solving quadratic and linear programming problems, which is derived from two salient existing neural networks. One of the predecessors has lower structural complexity but were not shown to be capable of solving degenerate QP problems including LP problems while the other does not have this limitation but has higer structural complexity. The proposed model inherits the merits of both models and thus serves as a competitive alternative for solving QP and LP problems. Numerical simulations are provided to demonstrate the performance of the model and validate the theoretical results.

[1]  Jinde Cao,et al.  Solving Quadratic Programming Problems by Delayed Projection Neural Network , 2006, IEEE Transactions on Neural Networks.

[2]  Nezam Mahdavi-Amiri,et al.  An efficient simplified neural network for solving linear and quadratic programming problems , 2006, Appl. Math. Comput..

[3]  Youshen Xia,et al.  A new neural network for solving linear and quadratic programming problems , 1996, IEEE Trans. Neural Networks.

[4]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[5]  Xiaolin Hu,et al.  A New Recurrent Neural Network for Solving Convex Quadratic Programming Problems With an Application to the $k$-Winners-Take-All Problem , 2009, IEEE Transactions on Neural Networks.

[6]  Xiaolin Hu,et al.  Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks , 2007, IEEE Transactions on Neural Networks.

[7]  Youshen Xia,et al.  An Extended Projection Neural Network for Constrained Optimization , 2004, Neural Computation.

[8]  Mauro Forti,et al.  Generalized neural network for nonsmooth nonlinear programming problems , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[10]  Shubao Liu,et al.  A Simplified Dual Neural Network for Quadratic Programming With Its KWTA Application , 2006, IEEE Transactions on Neural Networks.

[11]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network With a Discontinuous Hard-Limiting Activation Function for Quadratic Programming , 2008, IEEE Transactions on Neural Networks.

[12]  Xiaolin Hu,et al.  An Improved Dual Neural Network for Solving a Class of Quadratic Programming Problems and Its $k$-Winners-Take-All Application , 2008, IEEE Transactions on Neural Networks.

[13]  Xiaolin Hu,et al.  Design of General Projection Neural Networks for Solving Monotone Linear Variational Inequalities and Linear and Quadratic Optimization Problems , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  L. Liao,et al.  A neural network for monotone variational inequalities with linear constraints , 2003 .

[15]  Xing-Bao Gao,et al.  A novel neural network for nonlinear convex programming , 2004, IEEE Trans. Neural Networks.

[16]  Jinde Cao,et al.  A simple and high performance neural network for quadratic programming problems , 2001, Appl. Math. Comput..

[17]  Yunong Zhang,et al.  A dual neural network for convex quadratic programming subject to linear equality and inequality constraints , 2002 .

[18]  Nicholas G. Maratos,et al.  A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems , 2008, IEEE Transactions on Neural Networks.

[19]  Zhishun Wang,et al.  Constrained Least Absolute Deviation Neural Networks , 2008, IEEE Transactions on Neural Networks.