A project neural network for solving degenerate quadratic minimax problem with linear constraints

In this paper, a quadratic minimax problem with linear constraints is studied. The mixed linear constraints and the degeneracy are the two significant characters of the problem considered in this paper. On the basis of the project properties and Lyapunov method, we get the complete convergence and the finite-time convergence of the proposed neural network in this paper. Moreover, we get that the nonsingular parts of the output trajectories respect to Q"1"1 and Q"2"2 are exponentially convergent. Particularly, we also give some analysis to the degenerate quadratic minimax problem without constraints. Furthermore, four illustrative examples are given to show the necessity of the matrix H in the network to solve this problem and the superiority of the network in this paper.

[1]  Alaeddin Malek,et al.  Novel artificial neural network with simulation aspects for solving linear and quadratic programming problems , 2007, Comput. Math. Appl..

[2]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[3]  Youshen Xia,et al.  An improved neural network for convex quadratic optimization with application to real-time beamforming , 2005, Neurocomputing.

[4]  Wei Bian,et al.  A project neural network for solving degenerate convex quadratic program , 2007, Neurocomputing.

[5]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[6]  Abdesselam Bouzerdoum,et al.  Neural network for quadratic optimization with bound constraints , 1993, IEEE Trans. Neural Networks.

[7]  R. Rockafellar.  Linear-quadratic programming and optimal control , 1987 .

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

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

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

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

[12]  Tao Qing,et al.  The Neural Network Model for Solving Minimax Problems with Constraints , 2000 .

[13]  Jun Wang,et al.  A recurrent neural network with exponential convergence for solving convex quadratic program and related linear piecewise equations , 2004, Neural Networks.

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

[15]  J. Pang,et al.  On a Generalization of a Normal Map and Equation , 1995 .

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

[17]  Bingsheng He.  Solution and applications of a class of general linear variational inequalities , 1996 .

[18]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[19]  Xiaolin Hu,et al.  A Recurrent Neural Network for Solving a Class of General Variational Inequalities , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  L. Liao,et al.  A neural network for a class of convex quadratic minimax problems with constraints , 2004, IEEE Transactions on Neural Networks.

[21]  Zidong Wang,et al.  On global asymptotic stability of neural networks with discrete and distributed delays , 2005 .

[22]  Li-Zhi Liao,et al.  A Novel Neural Network for a Class of Convex Quadratic Minimax Problems , 2006, Neural Computation.