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Volumn 25, Issue 3, 2014, Pages 545-556

Neural network for nonsmooth, nonconvex constrained minimization via smooth approximation

Author keywords

Clarke stationary point; condition number; neural network; nonsmooth nonconvex optimization; smoothing approximation; variable selection

Indexed keywords

CONDITION NUMBERS; NONSMOOTH NONCONVEX OPTIMIZATION; SMOOTHING APPROXIMATION; STATIONARY POINTS; VARIABLE SELECTION;

EID: 84897640798     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2278427     Document Type: Article
Times cited : (59)

References (37)
  • 2
    • 0033354129 scopus 로고    scopus 로고
    • An analysis of a class of neural networks for solving linear programming problems
    • Nov.
    • E. K. P. Chong, S. Hui, and S. H. Zak, "An analysis of a class of neural networks for solving linear programming problems," IEEE Trans. Autom. Control, vol. 44, no. 11, pp. 1995-2005, Nov. 1999.
    • (1999) IEEE Trans. Autom. Control , vol.44 , Issue.11 , pp. 1995-2005
    • Chong, E.K.P.1    Hui, S.2    Zak, S.H.3
  • 3
    • 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. Neural Netw., vol. 51, no. 9, pp. 1741-1754, Sep. 2004.
    • (2004) IEEE Trans. Neural Netw. , vol.51 , Issue.9 , pp. 1741-1754
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 4
    • 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 ?ojasiewicz 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
  • 5
    • 49649119936 scopus 로고    scopus 로고
    • A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints
    • Aug.
    • Y. S. 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.S.1    Feng, G.2    Wang, J.3
  • 6
    • 67349167079 scopus 로고    scopus 로고
    • State estimation for coupled uncertain stochastic networks with missing measurements and timevarying delays: The discrete-time case
    • May
    • J. L. Liang, Z. D. Wang, and X. H. Liu, "State estimation for coupled uncertain stochastic networks with missing measurements and timevarying delays: The discrete-time case," IEEE Trans. Neural Netw., vol. 20, no. 5, pp. 781-793, May 2009.
    • (2009) IEEE Trans. Neural Netw. , vol.20 , Issue.5 , pp. 781-793
    • Liang, J.L.1    Wang, Z.D.2    Liu, X.H.3
  • 7
    • 67649321486 scopus 로고    scopus 로고
    • Subgradient-based neural network for nonsmooth nonconvex optimization problem
    • Jun.
    • W. Bian and X. P. Xue, "Subgradient-based neural network for nonsmooth nonconvex optimization problem," 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.P.2
  • 8
    • 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. S. 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.S.1    Wang, J.2
  • 9
    • 80052913883 scopus 로고    scopus 로고
    • A one layer recurrent neural network for constrained nonsmooth optimization
    • Oct.
    • Q. S. Liu and J. Wang, "A one layer recurrent neural network for constrained nonsmooth optimization," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 41, no. 5, pp. 1323-1333, Oct. 2011.
    • (2011) IEEE Trans. Syst. Man Cybern. B, Cybern. , vol.41 , Issue.5 , pp. 1323-1333
    • Liu, Q.S.1    Wang, J.2
  • 10
    • 79955864876 scopus 로고    scopus 로고
    • Recurrent neural network for non-smooth convex optimization problems with application to identification of genetic regulatory networks
    • May
    • L. Cheng, Z. G. Hou, Y. Z. Lin, M. Tan, W. C. Zhang, and F. X. Wu, "Recurrent neural network for non-smooth convex optimization problems with application to 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.G.2    Lin, Y.Z.3    Tan, M.4    Zhang, W.C.5    Wu, F.X.6
  • 11
    • 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
  • 12
    • 84865698786 scopus 로고    scopus 로고
    • Smoothing neural network for constrained non-Lipschitz optimization with applications
    • Mar.
    • W. Bian and X. Chen, "Smoothing neural network for constrained non-Lipschitz optimization with applications," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 3, pp. 399-411, Mar. 2012.
    • (2012) IEEE Trans. Neural Netw. Learn. Syst. , vol.23 , Issue.3 , pp. 399-411
    • Bian, W.1    Chen, X.2
  • 13
    • 0027187169 scopus 로고
    • Dynamic system identification using neural networks
    • Jan./Feb.
    • T. Yamada and T. Yabuta, "Dynamic system identification using neural networks," IEEE Trans. Syst. Man Cybern. B, Cybern., vol. 23, no. 1, pp. 204-211, Jan./Feb. 1993.
    • (1993) IEEE Trans. Syst. Man Cybern. B, Cybern. , vol.23 , Issue.1 , pp. 204-211
    • Yamada, T.1    Yabuta, T.2
  • 14
    • 58049205433 scopus 로고    scopus 로고
    • Convergence analysis of a class of nonsmooth gradient systems
    • Dec.
    • W. L. Lu and J. Wang, "Convergence analysis of a class of nonsmooth gradient systems," IEEE Trans. Circuits Syst. I, vol. 55, no. 11, pp. 3514-3527, Dec. 2008.
    • (2008) IEEE Trans. Circuits Syst. i , vol.55 , Issue.11 , pp. 3514-3527
    • Lu, W.L.1    Wang, J.2
  • 15
    • 1242308790 scopus 로고    scopus 로고
    • Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis
    • Jan.
    • H. D. Qi and L. Qi, "Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis," IEEE Trans. Circuits Syst. I, vol. 15, no. 1, pp. 99-109, Jan. 2004.
    • (2004) IEEE Trans. Circuits Syst. i , vol.15 , Issue.1 , pp. 99-109
    • Qi, H.D.1    Qi, L.2
  • 16
    • 33947725692 scopus 로고    scopus 로고
    • M-matrices and global convergence of discontinuous neural networks
    • DOI 10.1002/cta.381
    • M. Forti, "M-matrices and global convergence of discontinuous neural networks," Int. J. Circuit Theory Appl., vol. 35, no. 2, pp. 105-130, 2007. (Pubitemid 46506957)
    • (2007) International Journal of Circuit Theory and Applications , vol.35 , Issue.2 , pp. 105-130
    • Forti, M.1
  • 18
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. Ser. B, vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. R. Stat. Soc. Ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 19
    • 67650138146 scopus 로고    scopus 로고
    • Nonlinear filtering for sparse signal recovery from incomplete measurements
    • Jul.
    • L. B. Montefusco, D. Lazzaro, and S. Papi, "Nonlinear filtering for sparse signal recovery from incomplete measurements," IEEE Trans. Signal Process., vol. 57, no. 7, pp. 2494-2502, Jul. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.7 , pp. 2494-2502
    • Montefusco, L.B.1    Lazzaro, D.2    Papi, S.3
  • 20
    • 44449127493 scopus 로고    scopus 로고
    • Restricted isometry properties and nonconvex compressive sensing
    • R. Chartrand and V. Staneva, "Restricted isometry properties and nonconvex compressive sensing," Inverse Problems, vol. 24, no. 3, pp. 1-14, 2008.
    • (2008) Inverse Problems , vol.24 , Issue.3 , pp. 1-14
    • Chartrand, R.1    Staneva, V.2
  • 21
    • 84886302151 scopus 로고    scopus 로고
    • Worst-case complexity of smoothing quadratic regularization methods for non-Lipschitz optimization
    • SIAM Mar.
    • W. Bian and X. Chen, "Worst-case complexity of smoothing quadratic regularization methods for non-Lipschitz optimization," SIAM J. Optim., vol. 23, no. 3, pp. 1718-1741, Mar. 2013.
    • (2013) J. Optim. , vol.23 , Issue.3 , pp. 1718-1741
    • Bian, W.1    Chen, X.2
  • 23
    • 79957506054 scopus 로고    scopus 로고
    • Minimizing the condition number of a Gram matrix
    • SIAM Jan.
    • X. Chen, R. Womersley, and J. Ye, "Minimizing the condition number of a Gram matrix," SIAM J. Optim., vol. 21, pp. 127-148, Jan. 2011.
    • (2011) J. Optim. , vol.21 , pp. 127-148
    • Chen, X.1    Womersley, R.2    Ye, J.3
  • 24
    • 70450260767 scopus 로고    scopus 로고
    • Smoothing projected gradient method and its application to stochastic linear complementarity problems
    • SIAM
    • C. Zhang and X. Chen, "Smoothing projected gradient method and its application to stochastic linear complementarity problems," SIAM J. Optim., vol. 20, no. 2, pp. 627-649, 2009.
    • (2009) J. Optim. , vol.20 , Issue.2 , pp. 627-649
    • Zhang, C.1    Chen, X.2
  • 25
    • 84865690526 scopus 로고    scopus 로고
    • A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization
    • SIAM
    • F. E. Curtis and M. L. Overton, "A sequential quadratic programming algorithm for nonconvex, nonsmooth constrained optimization," SIAM J. Optim., vol. 22, no. 2, pp. 474-500, 2012.
    • (2012) J. Optim. , vol.22 , Issue.2 , pp. 474-500
    • Curtis, F.E.1    Overton, M.L.2
  • 26
    • 21144460519 scopus 로고
    • Nondifferentiable optimization via smooth approximation: General analytical approach
    • J. Kreimer and R. Y. Rubinstein, "Nondifferentiable optimization via smooth approximation: General analytical approach," Ann. Oper. Res., vol. 39, no. 1, pp. 97-119, 1992.
    • (1992) Ann. Oper. Res. , vol.39 , Issue.1 , pp. 97-119
    • Kreimer, J.1    Rubinstein, R.Y.2
  • 27
    • 58249142419 scopus 로고    scopus 로고
    • Application of a smoothing technique to decomposition in convex optimization
    • Dec.
    • I. Necoara and J. A. K. Suykens, "Application of a smoothing technique to decomposition in convex optimization," IEEE Trans. Autom. Control, vol. 53, no. 11, pp. 2674-2679, Dec. 2008.
    • (2008) IEEE Trans. Autom. Control , vol.53 , Issue.11 , pp. 2674-2679
    • Necoara, I.1    Suykens, J.A.K.2
  • 28
    • 84865682357 scopus 로고    scopus 로고
    • Smoothing methods for nonsmooth, nonconvex minimization
    • X. Chen, "Smoothing methods for nonsmooth, nonconvex minimization," Math. Program., vol. 134, no. 1, pp. 71-99, 2012.
    • (2012) Math. Program. , vol.134 , Issue.1 , pp. 71-99
    • Chen, X.1
  • 29
    • 0034148176 scopus 로고    scopus 로고
    • Smoothing methods for complementarity problems and their applications: A survey
    • X. Chen, "Smoothing methods for complementarity problems and their applications: A survey," J. Oper. Res. Soc. Jpn., vol. 43, no. 1, pp. 32-47, 2000.
    • (2000) J. Oper. Res. Soc. Jpn. , vol.43 , Issue.1 , pp. 32-47
    • Chen, X.1
  • 34
    • 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
  • 35
    • 82155173479 scopus 로고    scopus 로고
    • On Nesterov's nonsmooth Chebyshev-Rosenbrock functions
    • M. Gurbuzbalaban and M. L. Overton, "On Nesterov's nonsmooth Chebyshev-Rosenbrock functions," Nonlinear Anal., Theory Methods Appl., vol. 75, no. 3, pp. 1282-1289, 2012.
    • (2012) Nonlinear Anal., Theory Methods Appl. , vol.75 , Issue.3 , pp. 1282-1289
    • Gurbuzbalaban, M.1    Overton, M.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.