Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ

This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well-known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual solutions without applying additionally technical tools arising from Newton-techniques.