Global exponential stability of discrete-time recurrent neural network for solving quadratic programming problems subject to linear constraints

In this paper, a discrete-time recurrent neural network with global exponential stability is proposed for solving linear constrained quadratic programming problems. Compared with the existing neural networks for quadratic programming, the proposed neural network in this paper has lower model complexity with only one-layer structure. Moreover, the global exponential stability of the neural network can be guaranteed under some mild conditions. Simulation results with some applications show the performance and characteristic of the proposed neural network.

[1]  Qingshan Liu,et al.  Two k-winners-take-all networks with discontinuous activation functions , 2008, Neural Networks.

[2]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

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

[4]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[5]  Jun Wang,et al.  A one-layer recurrent neural network for support vector machine learning , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  María José Pérez-Ilzarbe.  Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints , 1998, IEEE Trans. Neural Networks.

[7]  Jun Wang,et al.  Global exponential stability of recurrent neural networks for solving optimization and related problems , 2000, IEEE Trans. Neural Networks Learn. Syst..

[8]  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.

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

[11]  Jinde Cao,et al.  A Novel Recurrent Neural Network With One Neuron and Finite-Time Convergence for $k$-Winners-Take-All Operation , 2010, IEEE Transactions on Neural Networks.

[12]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[13]  Jun Wang,et al.  A projection neural network and its application to constrained optimization problems , 2002 .

[14]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[15]  Shengwei Zhang,et al.  Lagrange programming neural networks , 1992 .

[16]  John J. Hopfield,et al.  Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit , 1986 .

[17]  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.

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

[19]  Jun Wang,et al.  A recurrent neural network for real-time matrix inversion , 1993 .

[20]  Alaeddin Malek,et al.  A discrete-time neural network for solving nonlinear convex problems with hybrid constraints , 2008, Appl. Math. Comput..

[21]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[22]  Haim Brezis.  Review: David Kinderlehrer and Guido Stampacchia, An introduction to variational inequalities and their applications , 1982 .

[23]  Qingshan Liu,et al.  A One-Layer Recurrent Neural Network with a Discontinuous Activation Function for Linear Programming , 2008, Neural Computation.

[24]  J Wang,et al.  Analysis and design of primal-dual assignment networks , 1998, IEEE Trans. Neural Networks.

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

[26]  Jun Wang,et al.  A dual neural network for kinematic control of redundant robot manipulators , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[27]  Kay Chen Tan,et al.  Global exponential stability of discrete-time neural networks for constrained quadratic optimization , 2004, Neurocomputing.

[28]  Xiaolin Hu,et al.  Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints , 2009, Neurocomputing.

[29]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .