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

Yang Li; Liwei Zhang

doi:10.3934/jimo.2009.5.651

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2009, Volume 5, Issue 3: 651-669. Doi: 10.3934/jimo.2009.5.651

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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
2.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, LiaoNing

Received: January 31, 2008

Revised: January 31, 2009

Published: June 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C22, 90C26; Secondary: 90C30.

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

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