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Saddle point and exact penalty representation for generalized proximal Lagrangians


  • Jinchuan Zhou


  • Naihua Xiu
  • Changyu Wang


In this paper, we introduce a generalized proximal Lagrangian function for the constrained nonlinear programming problem and discuss existence of its saddle points. In particular, the local saddle point is obtained by using the second-order sufficient conditions, and the global saddle point is given without requiring compactness of constraint set and uniqueness of the optimal solution. Finally, we establish equivalent relationship between global saddle points and exact penalty representations. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Jinchuan Zhou & Naihua Xiu & Changyu Wang, 2012. "Saddle point and exact penalty representation for generalized proximal Lagrangians," Journal of Global Optimization, Springer, vol. 54(4), pages 669-687, December.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:4:p:669-687
    DOI: 10.1007/s10898-011-9784-0

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    References listed on IDEAS

    1. Antanas Žilinskas, 2010. "On similarities between two models of global optimization: statistical models and radial basis functions," Journal of Global Optimization, Springer, vol. 48(1), pages 173-182, September.
    2. Pereyra, V. & Scherer, G., 2006. "Least squares collocation solution of elliptic problems in general regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 226-230.
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    Cited by:

    1. Changyu Wang & Qian Liu & Biao Qu, 2017. "Global saddle points of nonlinear augmented Lagrangian functions," Journal of Global Optimization, Springer, vol. 68(1), pages 125-146, May.


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