Computer Science ›› 2022, Vol. 49 ›› Issue (5): 227-234.doi: 10.11896/jsjkx.210400179

• Artificial Intelligence • Previous Articles     Next Articles

Novel Neural Network for Dealing with a Kind of Non-smooth Pseudoconvex Optimization Problems

YU Xin, LIN Zhi-liang   

  1. School of Computer,Electronics and Information,Guangxi University,Nanning 530004,China
  • Received:2021-04-19 Revised:2021-05-16 Online:2022-05-15 Published:2022-05-06
  • About author:YU Xin,born in 1973,Ph.D,professor,Ph.D supervisor,is a member of China Computer Federation.His main research interests include artificial neural network theory and optimization.
    LIN Zhi-liang,born in 1996,postgra-duate.His main research interests include neural network theory and so on.
  • Supported by:
    National Natural Science Foundation of China(61862004).

Abstract: The research of optimization problem is favored by researchers.Nonsmooth pseudoconvex optimization problems are a special kind of nonconvex optimization problems,which often appear in machine learning,signal processing,bioinformatics and various scientific and engineering fields.Based on the idea of penalty function and differential inclusion,a new neural network me-thod is proposed to solve the non-smooth pseudoconvex optimization problems with inequality constraints and equality constraints.Under given assumptions,the solution of the RNN can enter in the feasible region in finite time and stay there there-after,at last converge to the optimal solution set of the optimization problem.Compared with other neural networks,the RNN has the following advantages:1)simple structure,it is a single-layer model;2)it is not need to compute an exact penalty parameter in advance;3)the initial point is chosed arbitrarily.Under the environment of MATLAB,mathematical simulation experiments show that state solution can converge to the optimal solution.At the same time,if the initial points are not selected properly,the state solution will not converge in limit time even can not converge.This not only verifies the effectiveness of the proposed RNN,but also shows that the proposed network has a wider range of applications.

Key words: Differential inclusion, Nonsmooth pseudoconvex optimization, Optimal solution set, Penalty parameter, Recurrent neural network(RNN)

CLC Number: 

  • TP183
[1]MOKHTAR S B,HANIF D S,SHETTY C M.Nonlinear Programming Theory and Algorithms[M].New York:Wiley,1993.
[2]FRANK H C.Optimization and Nonsmooth Analysis[M].New York:Wilek,1983.
[3]AUBIN J P,FRANKOWSKA H.Set-Valued Analysis[M].Berlin:Birkuser,1990.
[4]FRANK H C.Optimization and Non-Smooth Analysis[M].New York:Wiley,1969.
[5]TANK D W,HOPFIELD 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.
[6]KENNEDY M P,CHUA L O.Neural networks for nonlinearprogramming[J].IEEE Transactions on Circuits and Systems,1988,35(5):554-562.
[7]ZHANG S,CONSTANTINIDES A G.Lagarange Programming Neural Networks[J].IEEE Transactions on Circuits and Systems.II,Analog Digit.Signal Process,1992,39(7):441-452.
[8]XIA Y,LEUNG H,WANG J.A projection neural network and its application to constrained optimization problems[J].IEEE Transactions on Circuits and Systems,2002,49(4):447-458.
[9]HU X,WANG J.An improved dual neural network for solving aclass of quadratic programming problems and its k-winners-take-all application[J].IEEE Transactions on Neural Networks,2008,19(12):2022-2031.
[10]LIU S,WANG J.A simplified dual neural network for quadratic programming with its KWTA application[J].IEEE Transactions on Neural Networks,2006,17(6):1500-1510.
[11]FORTI M,NISTRI P,QUINCAMPOIX M.Generalized neural network for nonsmooth nonlinear programming problems[J].IEEE Transactions on Circuits and Systems,2004,51(9):1741-1754.
[12]LI G,SONG S,WU C.Generalized gradient projection neuralnetworks for nonsmooth optimization problems[J].Science China on Information Sciences,2010,53(5):990-1005.
[13]XUE X P,BIAN W.Subgradient-based neural networks for nonsmooth convex optimization problems[J].IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(8):2378-2391.
[14]BIAN W,XUE X P.Subgradient-based neural networks for nonsmooth nonconvex optimization problems[J].IEEE Transactions on Neural Networks,2009,20(6):1024-1038.
[15]BIAN W,XUE X P.Neural network for solving constrainedconvex optimization problems with global attractivity[J].IEEE Transactions on Circuits and Systems,2013,60(3):710-723.
[16]QIN S T,FAN D,WU G,et al.Neural network for constrained nonsmooth optimization using Tikhonov regularization[J].Neural Networks,2015,63:272-281.
[17]QIN S T,XUE X P.A two-layer recurrent neural network for nonsmooth convex optimization problems[J].IEEE Transactions on Neural Networks and Learning Systems,2015,26(6):1149-1160.
[18]LIU Q,WANG J.A one-layer recurrent neural network for constrained nonsmooth optimization[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B (Cybernetics),2011,41(5):1323-1333.
[19]MARECHAL P,YE J J.Optimizing condition numbers[J].SIAM Journal on Optimization,2009,20(2):935-947.
[20]HU X,WANG J.Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network[J].IEEE Transactions on Neural Networks,2006,17(6):1487-1499.
[21]GUO Z,LIU Q,WANG J.A one-layer recurrent neural network for pseudoconvex optimization subject to linear equality constraints[J].IEEE Transactions on Neural Networks,2011,22(12):1892-1900.
[22]QIN S T,BIAN W,XUE X P.A new one layer recurrent neural network for nonsmooth pseudoconvex optimization[J].Neurocomputing,2013,120:655-662.
[23]LIU Q,GUO Z,WANG J.A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization[J].Neural Networks,2012,26:99-109.
[24]LI Q F,LIU Y Q,ZHU L K.Neural network for non-smooth pseudoconvex optimization with general constraints[J].Neurocomputing,2014,131:336-347.
[25]QIN S T,YANG X D,XUE X P,et al.A one layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints[J].IEEE Transactions on Cybernetics,2017,47(10):3063-3074.
[26]BIAN W,MA L T,QIN S T,et al.Neural network for non-smooth pseudoconvex optimization with general convex constraints[J].Neural Networks,2018,101:1-14.
[27]HOSSEINI A,WANG J,HOSSEINI S M.A recurrent neuralnetwork for solving a class of generalized convex optimization problems[J].Neural Networks,2013,44:78-86.
[28]CHENG L,HOU Z G,LIN Y Z,et al.Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks[J].IEEE Transactions on Neural Networks,2011,22(5):714-726.
[29]YU X,WU L Z,XU C H,et al.A novel neural network for solving nonsmooth nonconvex optimization problems[J].IEEE Transactions on Neural Networks and Learning Systems,2020,31(5):1475-1488.
[30]LI W J,BIAN W,XUE X P.Projected neural network for a class of Non-Lipschitz optimization problems with linear constraints[J].IEEE Transactions on Neural Networks and Learning Systems,2020,31(9):3361-3373.
[31]XU C,CHAI Y Y,QIN S T,et al.A neurodynamic approach to nonsmooth constrained pseudoconvex optimization problem[J].Neural Networks,2020,124:180-192.
[32]XIA Y S,WANG J,GUO W Z.Two projection neural networks with reduced model complexity for nonlinear programming[J].IEEE Transactions on Neural Networks and Learning Systems,2020,31(6):2020-2029.
[1] AN Xin, DAI Zi-biao, LI Yang, SUN Xiao, REN Fu-ji. End-to-End Speech Synthesis Based on BERT [J]. Computer Science, 2022, 49(4): 221-226.
[2] YU Xin, MA Chong, HU Yue, WU Ling-zhen, WANG Yan-lin. New Neural Network Method for Solving Nonsmooth Pseudoconvex Optimization Problems [J]. Computer Science, 2019, 46(11): 228-234.
Full text



No Suggested Reading articles found!