We prove that the classic logarithmic barrier problem is equivalent to a particular logarithmic barrier positive relaxation problem with barrier and scaling parameters. Based on the equivalence, a line-search primal-dual interior-point relaxation method for nonlinear programs is presented. Our method does not require any primal or dual iterates to be interior-points, which is prominently different from the existing interior-point methods in the literature. A new logarithmic barrier penalty function dependent on both primal and dual variables is used to prompt the global convergence of the method, where the penalty parameter is updated adaptively. Without assuming any regularity condition, it is proved that our method will terminate at an approximate KKT point of the original problem provided the barrier parameter tends zero. Otherwise, either an approximate infeasible stationary point or an approximate singular stationary point of the original problem will be found. Some preliminary nu 查看全文>>