Abstract
The k-winners-take-all (k-WTA) problem is to select k largest inputs from a set of inputs in a network, which has many applications in machine learning. The Cournot-Nash equilibrium is an important problem in economic models . The two problems can be formulated as linear variational inequalities (LVIs). In the paper, a linear case of the general projection neural network (GPNN) is applied for solving the resulting LVIs, and consequently the two practical problems. Compared with existing recurrent neural networks capable of solving these problems, the designed GPNN is superior in its stability results and architecture complexity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hopfield, J.J., Tank, D.W.: Computing with Neural Circuits: A Model. Science 233, 625–633 (1986)
Kennedy, M.P., Chua, L.O.: Neural Networks for Nonlinear Programming. IEEE Trans. Circuits Syst. 35, 554–562 (1988)
RodrÃguez-Vázquez, A., DomÃnguez-Castro, R., Rueda, A., Huertas, J.L., Sánchez-Sinencio, E.: Nonlinear Switched-Capacitor Neural Networks for Optimization Problems. IEEE Trans. Circuits Syst. 37, 384–397 (1990)
Tao, Q., Cao, J., Xue, M., Qiao, H.: A High Performance Neural Network for Solving Nonlinear Programming Problems with Hybrid Constraints. Physics Letters A 288, 88–94 (2001)
Xia, Y., Wang, J.: A Projection Neural Network and Its Application to Constrained Optimization Problems. IEEE Trans. Circuits Syst. I 49, 447–458 (2002)
Xia, Y., Wang, J.: A General Projection Neural Network for Solving Monotone Variational Inequalities and Related Optimization Problems. IEEE Trans. Neural Netw. 15, 318–328 (2004)
Xia, Y.: On Convergence Conditions of an Extended Projection Neural Network. Neural Computation 17, 515–525 (2005)
Hu, X., Wang, J.: Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network. IEEE Trans. Neural Netw. 17, 1487–1499 (2006)
Hu, X., Wang, J.: A Recurrent Neural Network for Solving a Class of General Variational Inequalities. IEEE Transactions on Systems, Man and Cybernetics - Part B: Cybernetics 37, 528–539 (2007)
Hu, X., Wang, J.: Solving Generally Constrained Generalized Linear Variational Inequalities Using the General Projection Neural Networks. IEEE Trans. Neural Netw. 18, 1697–1708 (2007)
Liu, S., Wang, J.: A Simplified Dual Neural Network for Quadratic Programming with Its KWTA Application. IEEE Trans. Neural Netw. 17, 1500–1510 (2006)
Pang, J.S., Yao, J.C.: On a Generalization of a Normal Map and Equations. SIAM J. Control Optim. 33, 168–184 (1995)
Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I and II. Springer, New York (2003)
Maass, W.: On the Computational Power of Winner-Take-All. Neural Comput. 12, 2519–2535 (2000)
Wolfe, W.J.: K-Winner Networks. IEEE Trans. Neural Netw. 2, 310–315 (1991)
Calvert, B.A., Marinov, C.: Another k-Winners-Take-All Analog Neural Network. IEEE Trans. Neural Netw. 11, 829–838 (2000)
Marinov, C.A., Hopfield, J.J.: Stable Computational Dynamics for a Class of Circuits with O(N) Interconnections Capable of KWTA and Rank Extractions. IEEE Trans. Circuits Syst. I 52, 949–959 (2005)
Nagurney, A., Zhang, D.: Projected Dynamical Systems and Variational Inequalities with Applications. Kluwer, Boston (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hu, X., Wang, J. (2008). Solving the k-Winners-Take-All Problem and the Oligopoly Cournot-Nash Equilibrium Problem Using the General Projection Neural Networks. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69158-7_73
Download citation
DOI: https://doi.org/10.1007/978-3-540-69158-7_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69154-9
Online ISBN: 978-3-540-69158-7
eBook Packages: Computer ScienceComputer Science (R0)