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Saddle point and exact penalty representation for generalized proximal Lagrangians

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  • Jinchuan Zhou
  • Naihua Xiu
  • Changyu Wang

Abstract

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

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    1. A. M. Rubinov & X. X. Huang & X. Q. Yang, 2002. "The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 775-791, November.
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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.
    2. M. V. Dolgopolik, 2018. "Augmented Lagrangian functions for cone constrained optimization: the existence of global saddle points and exact penalty property," Journal of Global Optimization, Springer, vol. 71(2), pages 237-296, June.

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