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Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems

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  • Y. S. Xia

    (Nanjing University of Posts and Telecommunications)

Abstract

The globally projected dynamical system has received considerable attention due to its low complexity for variational inequality and optimization computation. This paper obtains further results on the global convergence, asymptotic stability, and exponential stability of this system, respectively under monotonicity of the mapping, strict monotonicity of the mapping, and positive definiteness of the Jacobian matrix of the mapping. The new results obtained improve existing ones and cover the classical stability results of autonomous dynamical systems as special cases. An application to constrained optimization and complementarity problems is given to show the applied significance of the results obtained.

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  • Y. S. Xia, 2004. "Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 627-649, September.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:3:d:10.1023_b:jota.0000042598.21226.af
    DOI: 10.1023/B:JOTA.0000042598.21226.af
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    References listed on IDEAS

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    1. M. Pappalardo & M. Passacantando, 2002. "Stability for Equilibrium Problems: From Variational Inequalities to Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 567-582, June.
    2. Terry L. Friesz & David Bernstein & Nihal J. Mehta & Roger L. Tobin & Saiid Ganjalizadeh, 1994. "Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems," Operations Research, INFORMS, vol. 42(6), pages 1120-1136, December.
    3. Terry L. Friesz & David Bernstein & Roger Stough, 1996. "Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows," Transportation Science, INFORMS, vol. 30(1), pages 14-31, February.
    4. Y. S. Xia & J. Wang, 2000. "On the Stability of Globally Projected Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 129-150, July.
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    Cited by:

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    2. Ding, Ke & Huang, Nan-Jing, 2008. "A new class of interval projection neural networks for solving interval quadratic program," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 718-725.
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    5. Liu, Xiaolan & Zhou, Mi, 2016. "A one-layer recurrent neural network for non-smooth convex optimization subject to linear inequality constraints," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 39-46.

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