메뉴 건너뛰기




Volumn 24, Issue 5, 2013, Pages 812-824

A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints

Author keywords

Differential inclusion; Global convergence; Lyapunov function; Nonsmooth optimization; Projection neural network

Indexed keywords

DESIGN AND IMPLEMENTATIONS; DIFFERENTIAL INCLUSIONS; GLOBAL CONVER-GENCE; LINEAR EQUALITY CONSTRAINTS; NONSMOOTH OPTIMIZATION; NONSMOOTH OPTIMIZATION PROBLEMS; OPTIMIZATION PROBLEMS; PROJECTION NEURAL NETWORK;

EID: 84876337591     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2244908     Document Type: Article
Times cited : (228)

References (49)
  • 4
    • 67649321486 scopus 로고    scopus 로고
    • Subgradient-based neural networks for nonsmooth nonconvex optimization problems
    • Jun.
    • W. Bian and X. Xue, "Subgradient-based neural networks for nonsmooth nonconvex optimization problems," IEEE Trans. Neural Netw., vol. 20, no. 6, pp. 1024-1038, Jun. 2009.
    • (2009) IEEE Trans. Neural Netw. , vol.20 , Issue.6 , pp. 1024-1038
    • Bian, W.1    Xue, X.2
  • 5
    • 0027555144 scopus 로고
    • Neural network for quadratic optimization with bound constraints
    • DOI 10.1109/72.207617
    • A. Bouzerdoum and T. Pattison, "Neural network for quadratic optimization with bound constraints," IEEE Trans. Neural Netw., vol. 4, no. 2, pp. 293-304, Mar. 1993. (Pubitemid 23640394)
    • (1993) IEEE Transactions on Neural Networks , vol.4 , Issue.2 , pp. 293-304
    • Bouzerdoum, A.1    Pattison, T.R.2
  • 6
    • 79957506054 scopus 로고    scopus 로고
    • Minimizing the condition number of a Gram matrix
    • X. Chen, R. Womersley, and J. Ye, "Minimizing the condition number of a Gram matrix," SIAM J. Optim., vol. 21, no. 1, pp. 127-148, 2011.
    • (2011) SIAM J. Optim. , vol.21 , Issue.1 , pp. 127-148
    • Chen, X.1    Womersley, R.2    Ye, J.3
  • 7
    • 79955864876 scopus 로고    scopus 로고
    • Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks
    • May
    • L. Cheng, Z. Hou, Y. Lin, M. Tan, W. Zhang, and F. Wu, "Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks," IEEE Trans. Neural Netw., vol. 22, no. 5, pp. 714-726, May 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.5 , pp. 714-726
    • Cheng, L.1    Hou, Z.2    Lin, Y.3    Tan, M.4    Zhang, W.5    Wu, F.6
  • 8
    • 0033354129 scopus 로고    scopus 로고
    • Analysis of a class of neural networks for solving linear programming problems
    • DOI 10.1109/9.802909
    • E. Chong, S. Hui, and S. Zak, "An analysis of a class of neural networks for solving linear programming problems," IEEE Trans. Autom. Control, vol. 44, no. 11, pp. 1995-2006, Nov. 1999. (Pubitemid 30531636)
    • (1999) IEEE Transactions on Automatic Control , vol.44 , Issue.11 , pp. 1995-2006
    • Chong, E.K.P.1    Hui, S.2    Zak, S.H.3
  • 11
    • 31144460192 scopus 로고    scopus 로고
    • Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations
    • DOI 10.1016/j.physd.2005.12.006, PII S0167278905005063
    • M. Forti, M. Grazzini, P. Nistri, and L. Pancioni, "Generalized lyapunov approach for convergence of neural networks with discontinuous or nonlipschitz activations," Physica D, vol. 214, no. 1, pp. 88-99, 2006. (Pubitemid 43131061)
    • (2006) Physica D: Nonlinear Phenomena , vol.214 , Issue.1 , pp. 88-99
    • Forti, M.1    Grazzini, M.2    Nistri, P.3    Pancioni, L.4
  • 12
    • 0242696111 scopus 로고    scopus 로고
    • Global convergence of neural networks with discontinuous neuron activations
    • Nov.
    • M. Forti and P. Nistri, "Global convergence of neural networks with discontinuous neuron activations," IEEE Trans. Circuits Syst.-I, vol. 50, no. 11, pp. 1421-1435, Nov. 2003.
    • (2003) IEEE Trans. Circuits Syst.-I , vol.50 , Issue.11 , pp. 1421-1435
    • Forti, M.1    Nistri, P.2
  • 13
    • 28244452021 scopus 로고    scopus 로고
    • Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain
    • DOI 10.1109/TNN.2005.852862
    • M. Forti, P. Nistri, and D. Papini, "Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain," IEEE Trans. Neural Netwo., vol. 16, no. 6, pp. 1449-1463, Nov. 2005. (Pubitemid 41709643)
    • (2005) IEEE Transactions on Neural Networks , vol.16 , Issue.6 , pp. 1449-1463
    • Forti, M.1    Nistri, P.2    Papini, D.3
  • 14
    • 4744373635 scopus 로고    scopus 로고
    • Generalized neural network for nonsmooth nonlinear programming problems
    • Sep.
    • M. Forti, P. Nistri, and M. Quincampoix, "Generalized neural network for nonsmooth nonlinear programming problems," IEEE Trans. Circuits Syst.-I, vol. 51, no. 9, pp. 1741-1754, Sep. 2004.
    • (2004) IEEE Trans. Circuits Syst.-I , vol.51 , Issue.9 , pp. 1741-1754
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 15
    • 37849187126 scopus 로고    scopus 로고
    • Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality
    • DOI 10.1109/TNN.2006.879775
    • M. Forti, P. Nistri, and M. Quincampoix, "Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1471-1486, Nov. 2006. (Pubitemid 44824261)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1471-1486
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 16
    • 2542589347 scopus 로고    scopus 로고
    • A novel neural network for nonlinear convex programming
    • May
    • X. Gao, "A novel neural network for nonlinear convex programming," IEEE Trans. Neural Netw., vol. 15, no. 3, pp. 613-621, May 2004.
    • (2004) IEEE Trans. Neural Netw. , vol.15 , Issue.3 , pp. 613-621
    • Gao, X.1
  • 17
    • 34249016393 scopus 로고    scopus 로고
    • Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network
    • DOI 10.1109/TNN.2006.879774
    • X. Hu and J. Wang, "Solving pseudomonotone variational inequalities and pseudoconvex optimization problems using the projection neural network," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1487-1499, Nov. 2006. (Pubitemid 44824262)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1487-1499
    • Hu, X.1    Wang, J.2
  • 18
    • 35148879483 scopus 로고    scopus 로고
    • Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems
    • Oct.
    • X. Hu and J. Wang, "Design of general projection neural networks for solving monotone linear variational inequalities and linear and quadratic optimization problems," IEEE Trans. Sys., Man Cybern.-B, vol. 37, no. 5, pp. 1414-1421, Oct. 2007.
    • (2007) IEEE Trans. Sys., Man Cybern.-B , vol.37 , Issue.5 , pp. 1414-1421
    • Hu, X.1    Wang, J.2
  • 19
    • 57749106175 scopus 로고    scopus 로고
    • An improved dual neural network for solving a class of quadratic programming problems and its k-winners-take-all application
    • Dec.
    • X. Hu and J. Wang, "An improved dual neural network for solving a class of quadratic programming problems and its k-winners-take-all application," IEEE Trans. Neural Netw., vol. 19, no. 12, pp. 2022-2031, Dec. 2008.
    • (2008) IEEE Trans. Neural Netw. , vol.19 , Issue.12 , pp. 2022-2031
    • Hu, X.1    Wang, J.2
  • 20
    • 67349165051 scopus 로고    scopus 로고
    • A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winners-take-all problem
    • Apr.
    • X. Hu and B. Zhang, "A new recurrent neural network for solving convex quadratic programming problems with an application to the k-winners-take-all problem," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 654-664, Apr. 2009.
    • (2009) IEEE Trans. Neural Netw. , vol.20 , Issue.4 , pp. 654-664
    • Hu, X.1    Zhang, B.2
  • 21
    • 0024016062 scopus 로고
    • Neural networks for nonlinear programming
    • May
    • M. Kennedy and L. Chua, "Neural networks for nonlinear programming," IEEE Trans. Circuits Syst., vol. 35, no. 5, pp. 554-562, May 1988.
    • (1988) IEEE Trans. Circuits Syst. , vol.35 , Issue.5 , pp. 554-562
    • Kennedy, M.1    Chua, L.2
  • 23
    • 33745926792 scopus 로고    scopus 로고
    • A neural network model for nonsmooth optimization over a compact convex subset
    • G. Li, S. Song, C. Wu, and Z. Du, "A neural network model for nonsmooth optimization over a compact convex subset," in Proc. 3rd Int. Symp. Neural Netw., 2006, pp. 344-349.
    • Proc. 3rd Int. Symp. Neural Netw., 2006 , pp. 344-349
    • Li, G.1    Song, S.2    Wu, C.3    Du, Z.4
  • 24
    • 23044474397 scopus 로고    scopus 로고
    • A delayed neural network for solving linear projection equations and its analysis
    • DOI 10.1109/TNN.2005.849834
    • Q. Liu, J. Cao, and Y. Xia, "A delayed neural network for solving linear projection equations and its analysis," IEEE Trans. Neural Netw., vol. 16, no. 4, pp. 834-843, Jul. 2005. (Pubitemid 41064315)
    • (2005) IEEE Transactions on Neural Networks , vol.16 , Issue.4 , pp. 834-843
    • Liu, Q.1    Cao, J.2    Xia, Y.3
  • 25
    • 84855945623 scopus 로고    scopus 로고
    • A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for portfolio optimization
    • Feb.
    • Q. Liu, Z. Guo, and J. Wang, "A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for portfolio optimization," Neural Netw., vol. 26, pp. 99-109, Feb. 2012.
    • (2012) Neural Netw. , vol.26 , pp. 99-109
    • Liu, Q.1    Guo, Z.2    Wang, J.3
  • 26
    • 43449132396 scopus 로고    scopus 로고
    • A one-layer recurrent neural network with a discontinuous activation function for linear programming
    • Q. Liu and J. Wang, "A one-layer recurrent neural network with a discontinuous activation function for linear programming," Neural Comput., vol. 20, no. 5, pp. 1366-1383, 2008.
    • (2008) Neural Comput. , vol.20 , Issue.5 , pp. 1366-1383
    • Liu, Q.1    Wang, J.2
  • 27
    • 42549152732 scopus 로고    scopus 로고
    • A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming
    • DOI 10.1109/TNN.2007.910736
    • Q. Liu and J. Wang, "A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming," IEEE Trans. Neural Netw., vol. 19, no. 4, pp. 558-570, Apr. 2008. (Pubitemid 351583574)
    • (2008) IEEE Transactions on Neural Networks , vol.19 , Issue.4 , pp. 558-570
    • Liu, Q.1    Wang, J.2
  • 28
    • 70349138424 scopus 로고    scopus 로고
    • A one-layer recurrent neural network for nonsmooth convex optimization subject to linear equality constraints
    • Q. Liu and J. Wang, "A one-layer recurrent neural network for nonsmooth convex optimization subject to linear equality constraints," in Proc. 15th Int. Conf. Neural Inf. Proc. 2009, pp. 1003-1010.
    • Proc. 15th Int. Conf. Neural Inf. Proc. 2009 , pp. 1003-1010
    • Liu, Q.1    Wang, J.2
  • 29
    • 79953827554 scopus 로고    scopus 로고
    • Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions
    • Apr.
    • Q. Liu and J. Wang, "Finite-time convergent recurrent neural network with a hard-limiting activation function for constrained optimization with piecewise-linear objective functions," IEEE Trans. Neural Netw., vol. 22, no. 4, pp. 601-613, Apr. 2011.
    • (2011) IEEE Trans. Neural Netw. , vol.22 , Issue.4 , pp. 601-613
    • Liu, Q.1    Wang, J.2
  • 30
    • 80052913883 scopus 로고    scopus 로고
    • A one-layer recurrent neural network for constrained nonsmooth optimization
    • Oct.
    • Q. Liu and J. Wang, "A one-layer recurrent neural network for constrained nonsmooth optimization," IEEE Trans. Syst., Man, Cybern.-B, vol. 41, no. 5, pp. 1323-1333, Oct. 2011.
    • (2011) IEEE Trans. Syst., Man, Cybern.-B , vol.41 , Issue.5 , pp. 1323-1333
    • Liu, Q.1    Wang, J.2
  • 31
    • 34548629454 scopus 로고    scopus 로고
    • A simplified dual neural network for quadratic programming with its KWTA application
    • DOI 10.1109/TNN.2006.881046
    • S. Liu and J. Wang, "A simplified dual neural network for quadratic programming with its kwta application," IEEE Trans. Neural Netw., vol. 17, no. 6, pp. 1500-1510, Nov. 2006. (Pubitemid 44824263)
    • (2006) IEEE Transactions on Neural Networks , vol.17 , Issue.6 , pp. 1500-1510
    • Liu, S.1    Wang, J.2
  • 32
    • 33645706718 scopus 로고    scopus 로고
    • Dynamical behaviors of delayed neural network systems with discontinuous activation functions
    • DOI 10.1162/089976606775623324
    • W. Lu and T. Chen, "Dynamical behaviors of delayed neural network systems with discontinuous activation functions," Neural Comput., vol. 18, no. 3, pp. 683-708, 2006. (Pubitemid 43543835)
    • (2006) Neural Computation , vol.18 , Issue.3 , pp. 683-708
    • Lu, W.1    Chen, T.2
  • 33
    • 0026896765 scopus 로고
    • Linear and quadratic programming neural network analysis
    • Jul.
    • C. Maa and M. Shanblatt, "Linear and quadratic programming neural network analysis," IEEE Trans. Neural Netw., vol. 3, no. 4, pp. 580-594, Jul. 1992.
    • (1992) IEEE Trans. Neural Netw. , vol.3 , Issue.4 , pp. 580-594
    • Maa, C.1    Shanblatt, M.2
  • 35
    • 70450205215 scopus 로고    scopus 로고
    • Optimizing condition numbers
    • P. Maréchal and J. Ye, "Optimizing condition numbers," SIAM J. Optim., vol. 20, no. 2, pp. 935-947, 2010.
    • (2010) SIAM J. Optim. , vol.20 , Issue.2 , pp. 935-947
    • Maréchal, P.1    Ye, J.2
  • 36
    • 0031476882 scopus 로고    scopus 로고
    • Generalized convexity of functions and generalized monotonicity of set-valued maps
    • J. Penot and P. Quang, "Generalized convexity of functions and generalized monotonicity of set-valued maps," J. Optim. Theory Appl., vol. 92, no. 2, pp. 343-356, 1997.
    • (1997) J. Optim. Theory Appl. , vol.92 , Issue.2 , pp. 343-356
    • Penot, J.1    Quang, P.2
  • 37
    • 0022721216 scopus 로고
    • SIMPLE 'NEURAL' OPTIMIZATION NETWORKS: AN A/D CONVERTER, SIGNAL DECISION CIRCUIT, AND A LINEAR PROGRAMMING CIRCUIT
    • D. Tank and J. Hopfield, "Simple neural optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit," IEEE Trans. Circuits Syst., vol. 33, no. 5, pp. 533-541, May 1986. (Pubitemid 16595842)
    • (1986) IEEE transactions on circuits and systems , vol.CAS-33 , Issue.5 , pp. 533-541
    • Tank, D.W.1    Hopfield, J.J.2
  • 38
    • 0035903532 scopus 로고    scopus 로고
    • A high performance neural network for solving nonlinear programming problems with hybrid constraints
    • DOI 10.1016/S0375-9601(01)00542-4, PII S0375960101005424
    • Q. Tao, J. Cao, M. Xue, and H. Qiao, "A high performance neural network for solving nonlinear programming problems with hybrid constraints," Phys. Lett. A, vol. 288, no. 2, pp. 88-94, 2001. (Pubitemid 32927485)
    • (2001) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.288 , Issue.2 , pp. 88-94
    • Tao, Q.1    Cao, J.2    Xue, M.3    Qiao, H.4
  • 39
    • 0027659604 scopus 로고
    • Analysis and design of a recurrent neural network for linear programming
    • Sep.
    • J. Wang, "Analysis and design of a recurrent neural network for linear programming," IEEE Trans. Circuits Syst.-I, vol. 40, no. 9, pp. 613-618, Sep. 1993.
    • (1993) IEEE Trans. Circuits Syst.-I , vol.40 , Issue.9 , pp. 613-618
    • Wang, J.1
  • 40
    • 0028320687 scopus 로고
    • A deterministic annealing neural network for convex programming
    • J. Wang, "A deterministic annealing neural network for convex programming," Neural Netw., vol. 7, no. 4, pp. 629-641, 1994.
    • (1994) Neural Netw. , vol.7 , Issue.4 , pp. 629-641
    • Wang, J.1
  • 41
    • 49649119936 scopus 로고    scopus 로고
    • A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints
    • Aug.
    • Y. Xia, G. Feng, and J. Wang, "A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints," IEEE Trans. Neural Netw., vol. 19, no. 8, pp. 1340-1353, Aug. 2008.
    • (2008) IEEE Trans. Neural Netw. , vol.19 , Issue.8 , pp. 1340-1353
    • Xia, Y.1    Feng, G.2    Wang, J.3
  • 42
    • 0036539447 scopus 로고    scopus 로고
    • A projection neural network and its application to constrained optimization problems
    • Apr.
    • Y. Xia, H. Leung, and J. Wang, "A projection neural network and its application to constrained optimization problems," IEEE Trans. Circuits Syst.-I, vol. 49, no. 4, pp. 447-458, Apr. 2002.
    • (2002) IEEE Trans. Circuits Syst.-I , vol.49 , Issue.4 , pp. 447-458
    • Xia, Y.1    Leung, H.2    Wang, J.3
  • 43
    • 0032208805 scopus 로고    scopus 로고
    • A general methodology for designing globally convergent optimization neural networks
    • PII S1045922798088109
    • Y. Xia and J. Wang, "A general methodology for designing globally convergent optimization neural networks," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1331-1343, Nov. 1998. (Pubitemid 128742412)
    • (1998) IEEE Transactions on Neural Networks , vol.9 , Issue.6 , pp. 1331-1343
    • Xia, Y.1    Wang, J.2
  • 44
    • 0034227388 scopus 로고    scopus 로고
    • Global exponential stability of recurrent neural networks for solving optimization and related problems
    • Jul.
    • Y. Xia and J. Wang, "Global exponential stability of recurrent neural networks for solving optimization and related problems," IEEE Trans. Neural Netw., vol. 11, no. 4, pp. 1017-1022, Jul. 2000.
    • (2000) IEEE Trans. Neural Netw. , vol.11 , Issue.4 , pp. 1017-1022
    • Xia, Y.1    Wang, J.2
  • 45
    • 0035246390 scopus 로고    scopus 로고
    • A dual neural network for kinematic control of redundant robot manipulators
    • Feb.
    • Y. Xia and J. Wang, "A dual neural network for kinematic control of redundant robot manipulators," IEEE Trans. Syst., Man Cybern.-B, vol. 31, no. 1, pp. 147-154, Feb. 2001.
    • (2001) IEEE Trans. Syst., Man Cybern.-B , vol.31 , Issue.1 , pp. 147-154
    • Xia, Y.1    Wang, J.2
  • 46
    • 2442472146 scopus 로고    scopus 로고
    • A general projection neural network for solving monotone variational inequalities and related optimization problems
    • Mar.
    • Y. Xia and J. Wang, "A general projection neural network for solving monotone variational inequalities and related optimization problems," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 318-328, Mar. 2004.
    • (2004) IEEE Trans. Neural Netw. , vol.15 , Issue.2 , pp. 318-328
    • Xia, Y.1    Wang, J.2
  • 47
    • 15344350315 scopus 로고    scopus 로고
    • A recurrent neural network for solving nonlinear convex programs subject to linear constraints
    • DOI 10.1109/TNN.2004.841779
    • Y. Xia and J. Wang, "A recurrent neural network for solving nonlinear convex programs subject to linear constraints," IEEE Trans. Neural Netw., vol. 16, no. 2, pp. 379-386, Mar. 2005. (Pubitemid 40390821)
    • (2005) IEEE Transactions on Neural Networks , vol.16 , Issue.2 , pp. 379-386
    • Xia, Y.1    Wang, J.2
  • 48
    • 54749093290 scopus 로고    scopus 로고
    • Subgradient-based neural networks for nonsmooth convex optimization problems
    • Sep.
    • X. Xue and W. Bian, "Subgradient-based neural networks for nonsmooth convex optimization problems," IEEE Trans. Circuits Syst.-I, vol. 55, no. 8, pp. 2378-2391, Sep. 2008.
    • (2008) IEEE Trans. Circuits Syst.-I , vol.55 , Issue.8 , pp. 2378-2391
    • Xue, X.1    Bian, W.2
  • 49
    • 0026897309 scopus 로고
    • Lagrange programming neural networks
    • Jul.
    • S. Zhang and A. Constantinides, "Lagrange programming neural networks," IEEE Trans. Circuits Syst.-II, vol. 39, no. 7, pp. 441-452, Jul. 1992.
    • (1992) IEEE Trans. Circuits Syst.-II , vol.39 , Issue.7 , pp. 441-452
    • Zhang, S.1    Constantinides, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.