全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
-  2018 

求解具有约束的l1-范数问题的神经网络模型
A neural network for solving l1-norm problems with constraints

DOI: 10.6040/j.issn.1671-9352.0.2017.627

Keywords: l1-范数问题,神经网络,单层,稳定性,
l1-norm problem
,neural network,one-layer,stability

Full-Text   Cite this paper   Add to My Lib

Abstract:

摘要: 提出了一个解约束最小 l1-范数问题的单层神经网络模型。与已有神经网络模型相比,提出的模型所需神经元数少且层数少。通过引入 Lyapunov 函数,证明了该模型的稳定性和收敛性。数值试验结果表明所提出的模型具有良好的性能。
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

References

[1]  XIA Yousheng, KAMEL M. Cooperative recurrent neural networks for the constrained <i>L</i><sub>1</sub> estimator[J]. IEEE Transactions on Signal Processing, 2007, 55(7):3192-3206.
[2]  LIU Qingshan, WANG Jun. <i>L</i><sub>1</sub>-Minimization algorithms for sparse signal reconstruction based on a projection neural network[J]. IEEE Transactions on Neural Networks, 2016, 27(6):89-707.
[3]  XIA Yousheng, SUN Changyin, ZHENG Weixing. Discrete-time neural network for fast solving large linear <i>L</i><sub>1</sub> estimation problems and its application to image restoration[J]. IEEE Transactions on Neural Networks, 2012, 23(5):812-820.
[4]  XIA Yousheng. A compact cooperative recurrent neural network for computing general constrained <i>l</i><sub>1</sub> norm estimators[J]. IEEE Transactions on Signal Processing, 2009, 57(9):3693-3697.
[5]  LIU Qingshan, WANG Jun. A projection neural network for constrained quadratic minimax optimization[J]. IEEE Transactions on Neural Networks, 2015, 26:2891-2900.
[6]  GAO Xingbao, LIAO Lizhi. A neural network for monotone variational inequalities with linear constraints[J]. Physics Letters. A, 2003, 307(2):118-128.
[7]  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.
[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]  XUE Xiaoping, BIAN Wei. A project neural network for solving degenerate quadratic minimax problem with linear constraints[J]. Neurocomputing, 2009, 72:1826-1838.
[10]  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.
[11]  GAO Xingbao. A neural network for a class of extended linear variational inequalities[J]. Chinese Journal of Electronics, 2001, 10(4):471-475.
[12]  GAO Xingbao, LIAO Lizhi. A novel neural network for a class of convex quadratic minimax problems[J]. Neural Computation, 2006, 18(8):1818-1846.
[13]  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.
[14]  LI Cuiping, GAO Xingbao, LI Yawei, et al. A new neural network for <i>l</i><sub>1</sub>-norm programing[J]. Neurocomputing, 2016, 202:98-103.
[15]  KINDERLEHRER D, STAMPACCHIA G. An introduction to variational inequalities and their applications[M]. Salt Lake City: Academic Press, 1980.
[16]  HOPFIELD J J, TANK D W. Computing with neural circuits: a model[J]. Science, 1986, 233(4764):625-633.
[17]  XIA Yousheng, WANG Jun. Neural networks for solving least absolute and related problems[J]. Neurocomputing, 1998, 19:13-21.
[18]  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.
[19]  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.
[20]  ORTEGA J M, RHEINBOLDT W C. Iterative solution of nonlinear equation in several variables[M]. New York: Academic Press, 1970.
[21]  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.
[22]  TSENG P. A modified forward-backward splitting method for maximal monotone mappings[J]. SIAM Journal on Control and Optimization, 2000, 38(2): 431-446.
[23]  BERGER J O. Statistical decision theory and Bayesian analysis[M]. New York: Springer, 1985.
[24]  WANG Zhishun, PETERSON B S. Constrained least absolute deviation neural networks[J]. IEEE Transactions on Neural Networks, 2008, 19(2):273-283.
[25]  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.
[26]  GAO Xingbao. A novel neural network for nonlinear convex programming[J]. IEEE Transactions on Neural Networks, 2004, 15(3):613-621.
[27]  RUSZCZYNSHI A. Nonlinear optimization[M]. New Jersey: Princrton University Press, 2006
[28]  ZABCZYK J. Mathematical control theory: an introduction[M]. New York: Academic Press, 1992.
[29]  夏又生, 叶大振. 解<i>L</i><sub>1</sub>-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 <i>L</i><sub>1</sub>-norm minimization problem[J]. Acta Electronica Sinica, 1997, 25(11):99-102.
[30]  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.
[31]  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.
[32]  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.
[33]  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.
[34]  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.
[35]  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.
[36]  GAO Xingbao, LIAO Lizhi. A novel neural network for generally constrained variational inequalities[J]. Computers and Chemical Engineering, 2017, 104:1-10.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133