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Local Saddle Points and Convexification for Nonconvex Optimization Problems

Author

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  • Z. K. Xu

    (Zhejiang Normal University)

Abstract

Recently, Li (Ref. 1) obtained a saddle-point result for a general class of nonconvex optimization problems with inequality constraints, by using a transformation equivalent to taking the pth power of the objective function and the constraints, under several conditions. In this paper, we show that, by an equivalent transformation, using the pth power of the constraints or using the pth power of the objective function and the constraints, the same result can be obtained under much weaker and reasonable conditions. Also, our results can be extended to the problem in which equality and inequality constraints are involved.

Suggested Citation

  • Z. K. Xu, 1997. "Local Saddle Points and Convexification for Nonconvex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(3), pages 739-746, September.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:3:d:10.1023_a:1022613419816
    DOI: 10.1023/A:1022613419816
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    Cited by:

    1. Xiaoling Sun & Duan Li, 2000. "Asymptotic Strong Duality for Bounded Integer Programming: A Logarithmic-Exponential Dual Formulation," Mathematics of Operations Research, INFORMS, vol. 25(4), pages 625-644, November.
    2. H. Wu & H. Luo, 2012. "Saddle points of general augmented Lagrangians for constrained nonconvex optimization," Journal of Global Optimization, Springer, vol. 53(4), pages 683-697, August.
    3. 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.
    4. D. Li & X. L. Sun, 2000. "Local Convexification of the Lagrangian Function in Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 109-120, January.
    5. Francisco Guerra-Vázquez & Jan-J. Rückmann & Ralf Werner, 2012. "On saddle points in nonconvex semi-infinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 433-447, November.

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