An Alternative Recurrent Neural Network for Solving Variational Inequalities and Related Optimization Problems

There exist many recurrent neural networks for solving optimization-related problems. In this paper, we present a method for deriving such networks from existing ones by changing connections between computing blocks. Although the dynamic systems may become much different, some distinguished properties may be retained. One example is discussed to solve variational inequalities and related optimization problems with mixed linear and nonlinear constraints. A new network is obtained from two classical models by this means, and its performance is comparable to its predecessors. Thus, an alternative choice for circuits implementation is offered to accomplish such computing tasks.

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

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

[3]  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).

[4]  Long Cheng,et al.  Coordination of Two Redundant Robots Using a Dual Neural Network , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[5]  Shuzhi Sam Ge,et al.  A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

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

[8]  Long Cheng,et al.  A Neutral-Type Delayed Projection Neural Network for Solving Nonlinear Variational Inequalities , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[10]  Gang Feng,et al.  On Convergence Conditions of an Extended Projection Neural Network , 2005, Neural Computation.

[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]  Long Cheng,et al.  A Recurrent Neural Network for Hierarchical Control of Interconnected Dynamic Systems , 2007, IEEE Transactions on Neural Networks.

[13]  Mohamed S. Kamel,et al.  A Generalized Least Absolute Deviation Method for Parameter Estimation of Autoregressive Signals , 2008, IEEE Transactions on Neural Networks.

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

[15]  Elisa Ricci,et al.  Analog neural network for support vector machine learning , 2006, IEEE Transactions on Neural Networks.

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

[17]  Jun Wang,et al.  A general methodology for designing globally convergent optimization neural networks , 1998, IEEE Trans. Neural Networks.

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

[19]  Gang Feng,et al.  A new neural network for solving nonlinear projection equations , 2007, Neural Networks.

[20]  Gang Feng,et al.  Development and Analysis of a Neural Dynamical Approach to Nonlinear Programming Problems , 2007, IEEE Transactions on Automatic Control.

[21]  Jun Wang,et al.  Two neural network approaches to model predictive control , 2008, 2008 American Control Conference.

[22]  Jinde Cao,et al.  A Delayed Neural Network Method for Solving Convex Optimization Problems , 2006, Int. J. Neural Syst..

[23]  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.

[24]  Liqun Qi,et al.  A novel neural network for variational inequalities with linear and nonlinear constraints , 2005, IEEE Transactions on Neural Networks.

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

[26]  Xiaolin Hu,et al.  Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network , 2006, IEEE Transactions on Neural Networks.