计算机科学 ›› 2022, Vol. 49 ›› Issue (5): 227-234.doi: 10.11896/jsjkx.210400179
喻昕, 林植良
YU Xin, LIN Zhi-liang
摘要： 对优化问题的研究一直以来深受科研工作者的关注。非光滑伪凸优化作为非凸优化中的一类特殊问题,频繁出现在机器学习、信号处理、生物信息学以及各类科学与工程领域中,成为学者们研究的重点。基于罚函数以及微分包含的思想,提出了一种解决带有不等式约束条件和等式约束条件的非光滑伪凸优化问题的新型神经网络方法。在给定的假设条件下,该神经网络的解可以在有限时间内进入可行域并永驻其中,最终收敛到优化问题的最优解集。相比其他神经网络模型,该模型具有以下优点:1)结构简单,为单层模型;2)不需要事先计算精确的惩罚因子;3)初始点可任意选取。在MATLAB环境下,通过数值实验得出,所提网络都能在有限时间内收敛到一个最优解;而用现有的神经网络模型解决同样的优化问题时,若初始点选取不恰当,则会导致状态解不能在有效时间内收敛甚至不能收敛。这不仅进一步地验证了所提神经网络的有效性,同时也说明其具有更广泛的应用范围。
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| [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:Birkuser,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. |
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