# American Institute of Mathematical Sciences

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

 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.
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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