A globally and superlinearly convergent SQP algorithm for nonlinear constrained optimization

Based on a continuously differentiable exact penalty function and a regular ization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimi zation problems. The proposed algorithm incorporates automatic adjustment r ules for the choice of the parameters and makes use of an approximate direc tional derivative of the merit function to avoid the need to evaluate secon d order derivatives of the problem functions. Under mild assumptions the al gorithm is proved to be globally convergent, and in particular the superlin ear convergence rate is established without assuming that the strict comple mentarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising.