Further Discussions On An Interior-Point Method With Double Slack Vectors For Nonconvex Nonlinear Programming

We present a primal-dual interior-point algorithm with double slack vectors for solving nonlinear programming with inequality constraints. The algorithm uses an l₂—exact penalty function as the merit function and works entirely by line search to obtain new iterates. The penalty parameterρin the merit function is updated adaptively .With some given update rules for slack vectors and under suitable assumptions, we prove that, if the penalty parameterρis bounded for each barrier parameterμ, then any limit point of the sequence generated by algorithm is a Karush-Kuhn-Tucker point of the barrier subproblem; if the penalty parameterρis unbounded for some barrier parameterμ, then there is a limit point that is either a singular stationary point or a infeasible stationary point of the original problem.