Interior Point Algorithm for Constrained Sequential Max-Min Problems

摘要

To trace the aggregate homotopy method for constrained sequential max-min problems, a new interior point algorithm is proposed, and its global convergence is established under some conditions. The residual control criteria, which ensures that the obtained iterative points are interior points, is given by the condition that ensures the β-cone neighborhood to be included in the interior of the feasible region. Hence, the algorithm avoids judging whether the iterative points are the interior points or not in every predictor step and corrector step of the Euler-Newton method so that the computation is reduced greatly.