基于投影算子的回归神经网络模型及其在最优化问题中的应用

马儒宁; 陈天平

基于投影算子的回归神经网络模型及其在最优化问题中的应用

马儒宁^1,2,
陈天平²

1.
南京航空航天大学数学系,南京 210016;2.复旦大学数学研究所,上海 200433

详细信息

作者简介:
马儒宁(1976- ),男,山东济宁人,博士(联系人.Tel:+86-25-81672925;E-mail:mrning@nuaa.edu.cn)

中图分类号: O29；TP18
计量
- 文章访问数: 2916
- HTML全文浏览量: 193
- PDF下载量: 537
- 被引次数: 0
出版历程
- 收稿日期: 2004-03-24
- 修回日期: 2006-01-10
- 刊出日期: 2006-04-15

Recurrent Neural Network Model Based on Projective Operator and Its Application to Optimization Problems

MA Ru-ning^1,2,
CHEN Tian-ping²

1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China;

摘要

摘要: 研究了一种基于投影算子的神经网络模型．与以前研究投影算子的值域一般是n维欧氏空间中的紧凸子集不同，而是n维欧氏空间中未必有界的闭凸子集，同时目标函数也是一般的连续可微函数，未必为凸函数．证明了所研究的神经网络模型具有整体解轨道，以及当目标函数满足某些条件时解轨道的整体收敛性．此外，还将所研究的模型应用于闭凸约束极小化问题以及非线性互补问题和隐互补问题中，并通过数值模拟说明了该神经网络方法的有效性．
- 回归神经网络模型 /
- 投影算子 /
- 整体收敛性 /
- 最优化 /
- 互补问题
Abstract: The recurrent neural network (RNN) model based on projective operator is studied.Different from the former study,the value region of projective operator in the neural network which they study was a general closed convex subset of n demensional Euclidean space and it wasn't a compact convex set in general,that is,the value region of projective operator was probably unbounded.They prove that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions.After that,the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems.In addition,simulation experiments confirm the efficiency of the RNN.
- recurrent neural network model /
- projective operator /
- global convergence /
- optimization /
- complementarity problem

HTML全文

参考文献(15)

[1]	Hopfield J J,Tank D W.Neural computation of decision in optimization problem[J].Biol Cybern,1985,52(1):141—152.
[2]	Tank D W,Hopfield J J.Simple ‘neural’ optimization networks: an A/D converter, signal decision circuit, and a linear programming circuit[J].IEEE Trans Circuits Syst (Ⅰ),1988,35(5):554—562. doi: 10.1109/31.1783
[3]	Bouzerdoum A,Pattison T R.Neural network for quadratic optimization with bound constraints[J].IEEE Transactions on Neural Networks,1993,4(2):293—303. doi: 10.1109/72.207617
[4]	Perez-Ilzarbe M J.Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints[J].IEEE Transactions on Neural Networks,1998,9(6):1344—1351. doi: 10.1109/72.728385
[5]	Liang X B,Wang J.A recurrent neural network for nonlinear optimization with a continuosly differentiable objective function and bound constraints[J].IEEE Transactions on Neural Networks,2000,11(6):1251—1262. doi: 10.1109/72.883412
[6]	XIA You-shen,Leung Henry,WANG Jun.A projection neural network and its application to constrained optimization problems[J].IEEE Trans Circuits Syst (Ⅰ),2002,49(4):447—458. doi: 10.1109/81.995659
[7]	XIA You-shen,WANG Jun.A recurrent neural network for solving linear projection equations[J].Neural Networks,2000,13(3):337—350. doi: 10.1016/S0893-6080(00)00019-8
[8]	Liang X B.A recurrent neural network for nonlinear continuously differentiable optimization over a compact convex subset[J].IEEE Transactions on Neural Networks,2001,12(6):1487—1490. doi: 10.1109/72.963784
[9]	Liang X B.Qualitative analysis of a recurrent neural network for nonlinear continuously differentiable convex minimization over a nonempty closed convex subset[J].IEEE Transactions on Neural Networks,2001,12(6):1521—1525. doi: 10.1109/72.963790
[10]	Kinderlehrer D,Stampcchia G.An Introduction to Variational Inequalities and Their Applications[M].New York:Academic,1980.
[11]	Courant R,John F.Introduction to Calculus and Analysis[M].Vol 1.New York:Wiley,1989.
[12]	Fischer A.An NCP-function and its use for the solution of complementarity problems[A]In:Du D,Qi L,Womersley R,Eds.Recent Advance in Nonsmooth Optimization[C].New Jersey:World Scientific Publishers,1995,88—105.
[13]	Fischer A.New constrained optimization reformulation of complementarity problems[J].Journal of Optimization Theory and Applications,1998,97(1):105—117. doi: 10.1023/A:1022627217515
[14]	Qi H,Liao L.A smoothing Newton method for general nonlinear complementarity problems[J].Computational Optimization Applications,2000,17(2/3):231—253. doi: 10.1023/A:1026554432668
[15]	Kojima M,Shindo S.Extensions of Newton and quasi-Newton methods to systems of PC1 equations[J].J Oper Res Soc Jpn,1986,29:352—374.