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Local Convexification of the Lagrangian Function in Nonconvex Optimization

Author

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  • D. Li

    (Chinese University of Hong Kong)

  • X. L. Sun

    (Shanghai University, Jiading)

Abstract

It is well-known that a basic requirement for the development of local duality theory in nonconvex optimization is the local convexity of the Lagrangian function. This paper shows how to locally convexify the Lagrangian function and thus expand the class of optimization problems to which dual methods can be applied. Specifically, we prove that, under mild assumptions, the Hessian of the Lagrangian in some transformed equivalent problem formulations becomes positive definite in a neighborhood of a local optimal point of the original problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004628822745
    DOI: 10.1023/A:1004628822745
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. H. Z. Luo & G. Mastroeni & H. X. Wu, 2010. "Separation Approach for Augmented Lagrangians in Constrained Nonconvex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 275-290, February.
    2. Qian Liu & Wan Tang & Xin Yang, 2009. "Properties of saddle points for generalized augmented Lagrangian," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 111-124, March.

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