An efficient one-layer recurrent neural network for solving a class of nonsmooth optimization problems
Subject Areas : Statistics
Mohammad Javad
Ebadi
1
(Chabahar Maritime University/ Assistant Professor)
Alireza
Hosseini
2
(School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran/ Faculty member)
Hossein
Jafari
3
(Assistant , Professor, Chabahar Maritime University)
Keywords: شبکه عصبی بازگشتی, مسأله بهینهسازی محدب ناهموار, نامساوی غیرخطی, معادله خطی,
Abstract :
Constrained optimization problems have a wide range of applications in science, economics, and engineering. In this paper, a neural network model is proposed to solve a class of nonsmooth constrained optimization problems with a nonsmooth convex objective function subject to nonlinear inequality and affine equality constraints. It is a one-layer non-penalty recurrent neural network based on the differential inclusion. Unlike most of the existing neural network models, there is neither a penalty parameter nor a penalty function in its structure. It has less complexity which leads to the easier implementation of the model for solving optimization problems. The equivalence of optimal solutions set of the main optimization problem and the equilibrium points set of the model is proven. Moreover, the global convergence and the stability of the introduced neural network are shown. Some examples including the L1-norm minimization problem are given and solved by the proposed model to illustrate its performance and effectiveness.
[1] Tank, D. and Hopfield, J.J., 1986. Simple neural optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit. IEEE transactions on Circuits and Systems, 33(5), pp.533-541.
[2] Kennedy, M.P. and Chua, L.O., 1988. Neural networks for nonlinear programming. IEEE Transactions on Circuits and Systems, 35(5), pp.554-562.
[3] Zhang, S. and Constantinides, A.G.,1992 Lagrange programming neural networks. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 39(7), pp.441-452.
[4] Wang, J. and Xia, Y., 1998. Analysis and design of primal-dual assignment networks. IEEE Transactions on Neural Networks, 9(1), pp.183-194.
[5] Xia, Y., Leung, H. and Wang, J., 2002. A projection neural network and its application to constrained optimization problems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(4), pp.447-458.
[6] Xia, Y.S. and Wang, J., 2000. On the stability of globally projected dynamical systems. Journal of Optimization Theory and Applications, 106(1), pp.129-150.
[7] Liu, Q. and Wang, J., 2008a. A one-layer recurrent neural network with a discontinuous activation function for linear programming. Neural Computation, 20(5), pp.1366-1383.
[8] Liu, Q. and Wang, J., 2008b. A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming. IEEE Transactions on Neural Networks, 19(4), pp.558-570.
[9] Beliakov, G. and Bagirov, A., 2006. Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization Optimization, 55 (5), pp. 459-479.
