On saddle points of a class of augmented lagrangian functions

Qian Liu; Xinmin Yang; Heung Wing Joseph Lee

doi:10.3934/jimo.2007.3.693

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2007, Volume 3, Issue 4: 693-700. Doi: 10.3934/jimo.2007.3.693

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On saddle points of a class of augmented lagrangian functions

1.
Department of Mathematics, Inner Mongolia University, Hohhot, 010021
2.
Department of Mathematics, Chongqing Normal University, Chongqing 400047
3.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: October 31, 2006

Revised: March 31, 2007

Published: September 2007

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Abstract

For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.

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Mathematics Subject Classification: 90C26, 90C46.

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