American Institute of Mathematical Sciences

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July  2009, 5(3): 651-669. doi: 10.3934/jimo.2009.5.651

A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming

Yang Li 1, and  Liwei Zhang 2,

1. 

Department of Applied Mathematica, Dalian University of Technology, Dalian, Liaoning 116023, China
2. 

Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, LiaoNing

Received  February 2008 Revised  February 2009 Published  June 2009

We present a nonlinear Lagrangian method for nonconvex semidefinite programming. This nonlinear Lagrangian is generated by a Löwner operator associated with Log-Sigmoid function. Under a set of assumptions, we prove a convergence theorem, which shows that the nonlinear Lagrangian algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of the solution is proportional to the penalty parameter.
Keywords: Löwner operator., nonlinear Lagrangian, nonconvex semidefinite programming.
Mathematics Subject Classification: Primary: 90C22, 90C26; Secondary: 90C3.
Citation: Yang Li, Liwei Zhang. A nonlinear Lagrangian method based on Log-Sigmoid function for nonconvex semidefinite programming. Journal of Industrial & Management Optimization, 2009, 5 (3) : 651-669. doi: 10.3934/jimo.2009.5.651
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