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A new nonlinear Lagrangian method for nonconvex semidefinite programming

Li Y., Zhang L.

Journal of Applied Analysis

2009

Vol. 15, nr 2

149-172

We study convergence properties of a new nonlinear Lagrangian method for nonconvex semidefinite programming. The convergence analysis shows that this method converges locally when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter under the constraint nondegeneracy condition, the strict complementarity condition and the strong" second order sufficient conditions. The major tools used in the analysis include the second implicit function theorem and differentials of Lowner operators.