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Volumn 55, Issue 10, 2010, Pages 2347-2352

Dynamical analysis of neural networks of subgradient system

Author keywords

Constrained minima problem; nonsmooth ojasiewicz inequality; subgradient system

Indexed keywords

CONSTRAINED MINIMIZATION PROBLEM; DYNAMICAL ANALYSIS; EXISTENCE AND UNIQUENESS OF SOLUTION; MINIMA PROBLEM; NEURAL NETWORK MODEL; NON-SMOOTH; STABLE EQUILIBRIUM; SUBGRADIENT; TECHNICAL NOTES;

EID: 77957694291     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2052484     Document Type: Article
Times cited : (16)

References (24)
  • 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. Circuits Syst., vol. 51, no. 9, pp. 1741-1754, Sep. 2004.
    • (2004) IEEE Trans. Circuits Syst. , vol.51 , Issue.9 , pp. 1741-1754
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 4
    • 34547988902 scopus 로고    scopus 로고
    • Dynamical analysis of full-range cellular neural networks by exploiting differential variational inequalities
    • Nov.
    • G. D. Sandre, M. Forti, P. Nistri, and A. Premoli, "Dynamical analysis of full-range cellular neural networks by exploiting differential variational inequalities," IEEE Trans. Circuits Syst., vol. 54, no. 8, pp. 1736-1749, Nov. 2007.
    • (2007) IEEE Trans. Circuits Syst. , vol.54 , Issue.8 , pp. 1736-1749
    • Sandre, G.D.1    Forti, M.2    Nistri, P.3    Premoli, A.4
  • 5
    • 37849187126 scopus 로고    scopus 로고
    • Convergence of neural networks for programming problems via a nonsmooth Łojasiewicz inequality
    • Nov.
    • 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.
    • (2006) IEEE Trans. Neural Netw. , vol.17 , Issue.6 , pp. 1471-1486
    • Forti, M.1    Nistri, P.2    Quincampoix, M.3
  • 6
    • 54749093290 scopus 로고    scopus 로고
    • Subgradient-based neural networks for non-smooth convex optimization problems
    • Aug.
    • X. P. Xue and W. Bian, "Subgradient-based neural networks for non-smooth convex optimization problems,"IEEE Trans. Circuits Syst., vol. 55, no. 8, pp. 2378-2391, Aug. 2008.
    • (2008) IEEE Trans. Circuits Syst. , vol.55 , Issue.8 , pp. 2378-2391
    • Xue, X.P.1    Bian, W.2
  • 7
    • 36249023228 scopus 로고    scopus 로고
    • The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
    • J. Bolte, A. Daniilidis, and A. Lewis, "The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems," SIAM J. Optimiz., vol. 17, pp. 1205-1233, 2007.
    • (2007) SIAM J. Optimiz. , vol.17 , pp. 1205-1233
    • Bolte, J.1    Daniilidis, A.2    Lewis, A.3
  • 8
    • 33748133454 scopus 로고    scopus 로고
    • On the stable equilibrium points of gradient systems
    • P. A. Absil and K. Kurdyka, "On the stable equilibrium points of gradient systems," Syst. Control Lett., vol. 55, pp. 573-577, 2006.
    • (2006) Syst. Control Lett. , vol.55 , pp. 573-577
    • Absil, P.A.1    Kurdyka, K.2
  • 9
    • 0001228050 scopus 로고
    • Sur la géométrie semi-et sous-analytique
    • S. Łojasiewicz, "Sur la géométrie semi-et sous-analytique," Ann. Inst. Fourier, vol. 43, pp. 1575-1595, 1993.
    • (1993) Ann. Inst. Fourier , vol.43 , pp. 1575-1595
    • Łojasiewicz, S.1
  • 10
    • 67649088057 scopus 로고    scopus 로고
    • Global exponential stability and global convergence in finite time of neural networks with discontinuous activations
    • S. T. Qin and X. P. Xue, "Global exponential stability and global convergence in finite time of neural networks with discontinuous activations," Neural Process. Lett., vol. 29, pp. 189-204, 2009.
    • (2009) Neural Process. Lett. , vol.29 , pp. 189-204
    • Qin, S.T.1    Xue, X.P.2
  • 11
    • 0000741384 scopus 로고
    • Evolution equations with lack of convexity
    • M. Degiovanni, A. Marino, and M. Tosques, "Evolution equations with lack of convexity," Nonlin. Anal., vol. 9, pp. 1401-1443, 1985.
    • (1985) Nonlin. Anal. , vol.9 , pp. 1401-1443
    • Degiovanni, M.1    Marino, A.2    Tosques, M.3
  • 12
    • 58049206270 scopus 로고    scopus 로고
    • Lyapunov method and convergence of the full-range model of CNNs
    • Nov.
    • M. Di Marco, M. Forti, M. Grazzini, P. Nistri, and L. Pancioni, "Lyapunov method and convergence of the full-range model of CNNs," IEEE Trans. Circuits Syst., vol. 54, no. 11, pp. 3528-3541, Nov. 2008.
    • (2008) IEEE Trans. Circuits Syst. , vol.54 , Issue.11 , pp. 3528-3541
    • Di Marco, M.1    Forti, M.2    Grazzini, M.3    Nistri, P.4    Pancioni, L.5
  • 13
    • 0034310138 scopus 로고    scopus 로고
    • Proof of the gradient conjecture of R. Thom
    • K. Kurdyka, T. Mostowski, and A. Parusinski, "Proof of the gradient conjecture of R. Thom," Ann. Mathemat., vol. 152, pp. 763-792, 2000.
    • (2000) Ann. Mathemat. , vol.152 , pp. 763-792
    • Kurdyka, K.1    Mostowski, T.2    Parusinski, A.3
  • 14
    • 33646703294 scopus 로고    scopus 로고
    • A Sard theorem for non-differ-entiable functions
    • J. Bolte, A. Daniilidis, and A.S. Lewis, "A Sard theorem for non-differ-entiable functions," J. Math. Anal. Appl., vol. 321, pp. 729-740, 2006.
    • (2006) J. Math. Anal. Appl. , vol.321 , pp. 729-740
    • Bolte, J.1    Daniilidis, A.2    Lewis, A.S.3
  • 15
    • 67649321486 scopus 로고    scopus 로고
    • Subgradient-based neural networks for non-smooth nonconvex optimization problems
    • Jun.
    • W. Bian and X. P. Xue, "Subgradient-based neural networks for non-smooth 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.P.2
  • 16
    • 28244452021 scopus 로고    scopus 로고
    • Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain
    • Nov.
    • 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 Netw., vol. 16, no. 6, pp. 1449-1463, Nov. 2005.
    • (2005) IEEE Trans. Neural Netw. , vol.16 , Issue.6 , pp. 1449-1463
    • Forti, M.1    Nistri, P.2    Papini, D.3
  • 17
    • 58049205433 scopus 로고    scopus 로고
    • Convergence analysis of a class of nonsmooth gradient systems
    • Nov.
    • W. L. Lu and J. Wang, "Convergence analysis of a class of nonsmooth gradient systems," IEEE Trans. Circuits Syst., vol. 55, no. 11, pp. 3514-3527, Nov. 2008.
    • (2008) IEEE Trans. Circuits Syst. , vol.55 , Issue.11 , pp. 3514-3527
    • Lu, W.L.1    Wang, J.2
  • 18
    • 33847215093 scopus 로고    scopus 로고
    • On the properties of solutions to a differential inclusion associated with a nonsmooth constrained optimization problem
    • Seville, Spain, Dec. 12-15
    • P. Nistri and M. Quincampoix, "On the properties of solutions to a differential inclusion associated with a nonsmooth constrained optimization problem," in Proc. 44th IEEE Conf. Decision and Control and the European Control Conf. 2005, Seville, Spain, Dec. 12-15, 2005.
    • (2005) Proc. 44th IEEE Conf. Decision and Control and the European Control Conf. 2005
    • Nistri, P.1    Quincampoix, M.2
  • 19
    • 23844507126 scopus 로고    scopus 로고
    • Exceptional family of elements and solvability of variational inequalities for mappings defined only on closed convex cones in Banach spaces
    • J. L. Li and J. Whitaker, "Exceptional family of elements and solvability of variational inequalities for mappings defined only on closed convex cones in Banach spaces," J. Math. Anal. Appl., vol. 310, pp. 254-261, 2005.
    • (2005) J. Math. Anal. Appl. , vol.310 , pp. 254-261
    • Li, J.L.1    Whitaker, J.2
  • 20
    • 34247600645 scopus 로고    scopus 로고
    • On K-positivity properties of time-invariant linear systems subject to discrete point lags
    • M. De la Sen, "On K-positivity properties of time-invariant linear systems subject to discrete point lags," Positivity, vol. 11, pp. 319-340, 2007.
    • (2007) Positivity , vol.11 , pp. 319-340
    • De La Sen, M.1
  • 21
    • 0000332207 scopus 로고    scopus 로고
    • Reachable discrete-time positive systems with minimal dimension control sets
    • L. Caccetta and V. G. Rumchev, "Reachable discrete-time positive systems with minimal dimension control sets," Dynam. Continuous, Discrete Impuls. Syst., vol. 4, pp. 539-552, 1998.
    • (1998) Dynam. Continuous, Discrete Impuls. Syst. , vol.4 , pp. 539-552
    • Caccetta, L.1    Rumchev, V.G.2
  • 23
    • 2642559543 scopus 로고    scopus 로고
    • Continuous dynamical systems that realize discrete optimization on the hypercube
    • P.-A. Absil and R. Sepulchre, "Continuous dynamical systems that realize discrete optimization on the hypercube," Syst. Control Lett., vol. 52, pp. 297-304, 2004.
    • (2004) Syst. Control Lett. , vol.52 , pp. 297-304
    • Absil, P.-A.1    Sepulchre, R.2
  • 24
    • 0029358102 scopus 로고
    • Minimum-seeking properties of analog neural networks with multilinear objective functions
    • Aug.
    • M. Vidyasagar, "Minimum-seeking properties of analog neural networks with multilinear objective functions," IEEE Trans. Autom. Control, vol. 40, no. 8, pp. 1359-1375, Aug. 1995.
    • (1995) IEEE Trans. Autom. Control , vol.40 , Issue.8 , pp. 1359-1375
    • Vidyasagar, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.