Abstract
This paper introduces a projection-based generalized neural network, which can be used to solve a class of nonsmooth convex optimization problems. It generalizes the existing projection neural networks for solving the optimization problems. In addition, the existence and convergence of the solution for the generalized neural networks are proved. Moreover, we discuss the application to nonsmooth convex optimization problems. And two illustrative examples are given to show the efficiency of the theoretical results.
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References
Liu, Q., Cao, J., Xia, Y.: A delayed neural network for solving linear projection equations and its analysis. IEEE Trans. Neu. Net. 16, 834–843 (2005)
Xia, Y., Feng, G.: On convergence conditions of an extended projection neural network. Neu. Comp. 16, 515–525 (2005)
Ma, R., Chen, T.: Recurrent neural network model based on projective operator and its application to optimization problems. Appl. Math. Mech. 27(4), 543–554 (2006)
Yang, Y., Cao, J.: A delayed neural network method for solving convex optimization problems. IJNS 16(4), 295–303 (2006)
Hu, X.: Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraits. Neu. Comp. 72, 1131–1137 (2009)
Xia, Y., Feng, G.: A new neural network for solving nonlinear projection equations. Neu. Net. 20, 577–589 (2007)
Gao, X., Liao, L.: A new projection-based neural network for constrained variational inequalities. IEEE Trans. Neu. Net. 20(3), 373–388 (2009)
Forti, M., Nistri, P., Quincampoix, M.: Generalized neural nerwork for nonsmooth nonlinear programming problems. IEEE Trans. Cir. 51(9), 1741–1754 (2004)
Forti, M., Nistri, P.: Global convergence of neural networks with discontinuous neuron activations. IEEE Trans. Cir. 50(11), 1421–1435 (2003)
Kennedy, M.P., Chua, L.: Neural network for nonlinear programming. IEEE Trans. Cir. 35(5), 554–562 (1988)
Forti, M., Nistri, P., Quincampoix, M.: Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality. IEEE Trans. Neu. Net. 17(6), 1471–1486 (2006)
Liu, Q., Wang, J.: A one-layer recurrent neural network with a discontinuous activation function for linear programming. Neu. Comp. 20, 1366–1383 (2008)
Liu, Q., Wang, J.: A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming. IEEE Trans. Neu. Net. 19(4), 558–570 (2008)
Cheng, L., Hou, Z., Tan, M., Wang, X., Zhao, Z., Hu, S.: A recurrent neural network for non-smooth nonlinear programming problems. In: IJCNN 2007, pp. 12–17 (2007)
Xue, X., Bian, W.: Subgradient-based neural networks for nonsmooth convex optimization problems. IEEE Trans. Cir. 55(8), 2378–2391 (2008)
Bian, W., Xue, X.: Subgradient-based neural networks for nonsmooth nonconvex optimization problems. IEEE Trans. Neu. Net. 20(6), 1024–1038 (2009)
Noor, M.A., Wang, Y., Xiu, N.: Some new projection methods for variational inequalities. Appl. Mathe. Comput. 137, 423–435 (2003)
Lu, W., Wang, J.: Convergence analysis of a class of nonsmooth gradient systems. IEEE Trans. Cir. 55(11), 3514–3527 (2008)
Clarke, F.H.: Optimization, nonsmooth analysis. John Wiley Sons, Chichester (1983)
Aubin, J.P., Cellina, A.: Differential inclusions. Springer, Heidelberg (1984)
Aubin, J.P.: Viability Theory. Birhäuser, Cambridge (1991)
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Liu, J., Yang, Y., Xu, X. (2010). Convergence of the Projection-Based Generalized Neural Network and the Application to Nonsmooth Optimization Problems. In: Zhang, L., Lu, BL., Kwok, J. (eds) Advances in Neural Networks - ISNN 2010. ISNN 2010. Lecture Notes in Computer Science, vol 6063. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13278-0_33
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DOI: https://doi.org/10.1007/978-3-642-13278-0_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13277-3
Online ISBN: 978-3-642-13278-0
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