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

We present a primal-dual interior-point algorithm for solving optimization problems with nonlinear inequality constraints. The algorithm works entirely by line search to obtain new iterates. The method uses an l₂—exact penalty function as the merit function. Our analysis shows that under standard assumptions, the method has strong global convergence properties. The penalty parameterρin the merit function is updated adaptively. It is shown that if penalty parameterρis bounded for each barrier parameterμ, then any limit point of the sequence generated by the 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. We present some numerical results to confirm that the algorithm produces the correct results for some hard problems.