Abstract
In this paper, a projection neural network for solving convex optimization is investigated. Using Lyapunov stability theory and LaSalle invariance principle, the proposed network is showed to be globally stable and converge to exact optimal solution. Two examples show the effectiveness of the proposed neural network model.
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References
Tank, D.W., Hopfield, J.J.: Simple ‘Neural’ Optimization Network: An A/D Converter, Signal Decision Circuit and A Linear Programming Circuit. IEEE Trans. Circuits Syst. 33, 533–541 (1986)
Kennedy, M.P., Chua, L.O.: Neural Networks for Nonlinear Programming. IEEE Trans. Circuits Syst. 35, 554–562 (1988)
Chen, K.Z., Leung, Y., Leung, K.S., Gao, X.B.: A Neural Network for Solving Nonlinear Programming Problem. Neural Comput. and Applica. 11, 103–111 (2002)
Xia, Y., Wang, J.: A Recurrent Neural Networks for Nonlinear Convex Optimization Subject to Nonlinear Inequality Constraints. IEEE Trans. Circuits Syst.-I 51, 1385–1394 (2004)
Gao, X.B.: A Novel Neural Network for Nonlinear Convex Programming. IEEE Trans. Neural Networks 15, 613–621 (2004)
Zhang, Y., Wang, J.: A Dual Neural Network for Convex Quadratic Programming Subject to Linear Equality and Inequality Constraints. Phys. Lett. A 298, 271–278 (2002)
Tao, Q., Cao, J., Xue, M., Qiao, H.: A High Performance Neural Network for Solving Nonlinear Programming Problems with Hybrid Constraints. Phys. Lett. A 288, 88–94 (2001)
Liu, Q., Cao, J., Xia, Y.: A Delayed Neural Network for Solving Linear Projection Equations and Its Analysis. IEEE Trans. Neural Networks 16, 834–843 (2005)
Yang, Y., Cao, J.: Solving Quadratic Programming Problems by Delayed Projection Neural Network. IEEE Trans. Neural Networks 17, 1630–1634 (2006)
Yang, Y., Cao, J.: A Delayed Neural Network Method for Solving Convex Optimization Problems. Intern. J. Neural Sys. 16, 295–303 (2006)
Yang, Y., Xu, Y., Zhu, D.: The Neural Network for Solving Convex Nonlinear Programming Problem. In: Huang, D.-S., Li, K., Irwin, G.W. (eds.) ICIC 2006. LNCS, vol. 4113, pp. 494–499. Springer, Heidelberg (2006)
Xia, Y., Feng, G., Wang, J.: A Recurrent Neural Networks with Exponential Convergence for Solving Convex Quadratic Program and Related Linear Piecewise Equations. Neural Networks, 17, 1003–1015 (2004)
Liu, Q., Wang, J., Cao, J.: A Delayed Lagrangian Network for Solving Quadratic Programming Problems with Equality Constraints. In: Wang, J., Yi, Z., Zurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3971, pp. 369–378. Springer, Heidelberg (2006)
Hu, X., Wang, J.: Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network. IEEE Trans. Neural Networks 17, 1487–1499 (2006)
Friesz, T.L., Bernstein, D.H., Mehta, N.J., Tobin, R.L., Ganjlizadeh, S.: Day-to-day Dynamic Network Disequilibria and Idealized Traveler Information Systems. Opera. Rese. 42, 1120–1136 (1994)
Kinderlehrer, D., Stampcchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic, New York (1980)
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Yang, Y., Xu, X. (2007). The Projection Neural Network for Solving Convex Nonlinear Programming. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_20
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DOI: https://doi.org/10.1007/978-3-540-74205-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74201-2
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