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

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


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