A robust SQP method based on a smoothing lower order penalty function†

Based on a smoothing approximation of a lower order penalty function and following Facchinei's method of dealing with the inconsistency of subproblems in SQP methods, we present a new robust SQP algorithm for solving a nonlinear constrained optimization problem. The proposed algorithm incorporates automatic adjustment rules for the choice of parameters. Under a new regularity condition at infeasible points, the algorithm is proved to be globally convergent.