Convergence analysis of a nonlinear Lagrangian method for nonconvex semidefinite programming with subproblem inexactly solved

Abstract

In this paper, we analyze the convergence properties of anonlinear Lagrangian method based on Log-Sigmoid function fornonconvex semidefinite programming (NCSDP) problems. It isdifferent from other convergence analysis, because the subproblemin our algorithm is inexactly solved. Under the constraintnondegeneracy condition, the strict complementarity condition andthe second order sufficient conditions, it is obtained that thenonlinear Lagrangian algorithm proposed is locally convergent bychoosing a proper stopping criterion and the error bound ofsolution is proportional to the penalty parameter when the penaltyparameter is less than a threshold.