American Institute of Mathematical Sciences

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October  2007, 3(4): 693-700. doi: 10.3934/jimo.2007.3.693

On saddle points of a class of augmented lagrangian functions

Qian Liu 1, , Xinmin Yang 2, and  Heung Wing Joseph Lee 3,

1. 

Department of Mathematics, Inner Mongolia University, Hohhot, 010021, China
2. 

Department of Mathematics, Chongqing Normal University, Chongqing 400047
3. 

Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received  November 2006 Revised  April 2007 Published  October 2007

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.
Keywords: augmented Lagrangian function., saddle point, Nonconvex optimization.
Mathematics Subject Classification: 90C26, 90C4.
Citation: Qian Liu, Xinmin Yang, Heung Wing Joseph Lee. On saddle points of a class of augmented lagrangian functions. Journal of Industrial & Management Optimization, 2007, 3 (4) : 693-700. doi: 10.3934/jimo.2007.3.693
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