JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 90-98.doi: 10.6040/j.issn.1671-9352.0.2017.627

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A neural network for solving l1-norm problems with constraints

LI Cui-ping, GAO Xing-bao*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: This paper presents a one-layer neural network model for solving l1-norm problems with constraints. Compared with some existing neural network models, the proposed model needs fewer neurons and has a simpler structure. The stability and convergence of the proposed model are proved by introducing a Lyapunov function. Some simulation examples are used to illustrate its validity and transient behaviors.

Key words: l1-norm problem, neural network, one-layer, stability

CLC Number: 

  • O241.6
[1] KINDERLEHRER D, STAMPACCHIA G. An introduction to variational inequalities and their applications[M]. Salt Lake City: Academic Press, 1980.
[2] ORTEGA J M, RHEINBOLDT W C. Iterative solution of nonlinear equation in several variables[M]. New York: Academic Press, 1970.
[3] SOLODOV M V, TSENG P. Modified projection-type methods for monotone variational inequalities[J]. SIAM Journal on Control and Optimization, 1996, 34(5): 1814-1830.
[4] TSENG P. A modified forward-backward splitting method for maximal monotone mappings[J]. SIAM Journal on Control and Optimization, 2000, 38(2): 431-446.
[5] BERGER J O. Statistical decision theory and Bayesian analysis[M]. New York: Springer, 1985.
[6] HARKER P T, PANG Jongshi. Finite dimensional variational inequality and nonlinear complementarity problem: a survey of theory, algorithms, and applications[J]. Math Program: Series B, 1990, 48:161-220.
[7] HOPFIELD J J, TANK D W. Computing with neural circuits: a model[J]. Science, 1986, 233(4764):625-633.
[8] TANK D W, HOPFIELD J J. Simple neural optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit[J]. IEEE Transactions on Circuits and Systems, 1986, 33(5):533-541.
[9] 夏又生, 叶大振. 解L1-范数极小化问题的神经网络[J]. 电子学报, 1997, 25(11):99-102. XIA Yousheng, YE Dazhen. Neural network for solving L1-norm minimization problem[J]. Acta Electronica Sinica, 1997, 25(11):99-102.
[10] XIA Yousheng, WANG Jun. Neural networks for solving least absolute and related problems[J]. Neurocomputing, 1998, 19:13-21.
[11] WANG Zhishun, CHEUNG J, XIA Yousheng, et al. Minimum fuel neural networks and their applications to overcomplete signal representations[J]. IEEE Transactions on Fundamental Theory and Applications, 2000, 47(8):1146-1159.
[12] WANG Zhishun, HE Zhenya, CHEN Jiande. Robust time delay estimation of bioelectric signals[J]. IEEE Transactions on Bio-medical Engineering, 2005, 52(3):454-462.
[13] WANG Zhishun, PETERSON B S. Constrained least absolute deviation neural networks[J]. IEEE Transactions on Neural Networks, 2008, 19(2):273-283.
[14] XIA Yousheng, KAMEL M. Cooperative recurrent neural networks for the constrained L1 estimator[J]. IEEE Transactions on Signal Processing, 2007, 55(7):3192-3206.
[15] XIA Yousheng, KAMEL M. A generalized least absolute deviation method for parameter estimation of autoregressive signals[J]. IEEE Transactions on Neural Networks, 2008, 19(1):107-118.
[16] LIU Qingshan, WANG Jun. L1-Minimization algorithms for sparse signal reconstruction based on a projection neural network[J]. IEEE Transactions on Neural Networks, 2016, 27(6):89-707.
[17] XIA Yousheng, SUN Changyin, ZHENG Weixing. Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration[J]. IEEE Transactions on Neural Networks, 2012, 23(5):812-820.
[18] LI Cuiping, GAO Xingbao, LI Yawei, et al. A new neural network for l1-norm programing[J]. Neurocomputing, 2016, 202:98-103.
[19] XIA Yousheng. A compact cooperative recurrent neural network for computing general constrained l1 norm estimators[J]. IEEE Transactions on Signal Processing, 2009, 57(9):3693-3697.
[20] GAO Xingbao. A novel neural network for nonlinear convex programming[J]. IEEE Transactions on Neural Networks, 2004, 15(3):613-621.
[21] LIU Qingshan, WANG Jun. A projection neural network for constrained quadratic minimax optimization[J]. IEEE Transactions on Neural Networks, 2015, 26:2891-2900.
[22] XUE Xiaoping, BIAN Wei. A project neural network for solving degenerate quadratic minimax problem with linear constraints[J]. Neurocomputing, 2009, 72:1826-1838.
[23] HU Xiaolin. Applications of the general projection neural network in solving extended linear-quadratic programming problems with linear constraints[J]. Neurocomputing, 2009, 72:1131-1137.
[24] QIN Sitian, LE Xinyi, WANG Jun. A neurodynamic optimization approach to bilevel quadratic programming[J]. IEEE Transactions on Neural Networks, 2017, 28(11):2580-2591.
[25] LE Xinyi, WANG Jun. A two-time-scale neurodynamic approach to constrained minimax optimization[J]. IEEE Transactions on Neural Networks, 2017, 28(3):620-629.
[26] GAO Xingbao, LI Cuiping. A new neural network for convex quadratic minimax problems with box and equality constraints[J]. Computers and Chemical Engineering, 2017, 104:1-10.
[27] GAO Xingbao. A neural network for a class of extended linear variational inequalities[J]. Chinese Journal of Electronics, 2001, 10(4):471-475.
[28] GAO Xingbao, LIAO Lizhi. A neural network for monotone variational inequalities with linear constraints[J]. Physics Letters. A, 2003, 307(2):118-128.
[29] DU Lili, GAO Xingbao. A neural network with finite-time convergence for a class of variational inequalities[C] // International Conference on Intelligent Computing. New York: Springer, 2006, 4113:32-41.
[30] GAO Xingbao, LIAO Lizhi. A new projection-based neural network for constrained variational inequalities[J]. IEEE Transactions on Neural Networks, 2009, 15(4):622-628.
[31] GAO Xingbao, LIAO Lizhi. A novel neural network for generally constrained variational inequalities[J]. Computers and Chemical Engineering, 2017, 104:1-10.
[32] GAO Xingbao, LIAO Lizhi. A novel neural network for a class of convex quadratic minimax problems[J]. Neural Computation, 2006, 18(8):1818-1846.
[33] HU Xiaolin, SUN Changyin, ZHANG Bo. Design of recurrent neural networks for solving constrained least absolute deviation problems[J]. IEEE Transactions on Neural Networks, 2010, 21(7):1073-1086.
[34] RUSZCZYNSHI A. Nonlinear optimization[M]. New Jersey: Princrton University Press, 2006
[35] ZABCZYK J. Mathematical control theory: an introduction[M]. New York: Academic Press, 1992.
[36] GAO Xingbao, LIAO Lizhi. A new one-layer network for linear and quadratic programming[J]. IEEE Transactions on Neural Networks, 2010, 21(6):918-929.
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