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

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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

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

Abstract
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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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