Summary: Transition to superlinear local convergence is shown for a modified version of the trust-region filter-SQP method for nonlinear programming introduced by R. Fletcher, S. Leyffer
and Ph. L. Toint
[SIAM J. Optim. 13, No. 1, 44–59 (2002; Zbl 1029.65063
)]. Hereby, the original trust-region SQP-steps can be used without an additional second order correction. The main modification consists in using the Lagrangian function value instead of the objective function value in the filter together with an appropriate infeasibility measure. Moreover, it is shown that the modified trust-region filter-SQP method has the same global convergence properties as the original algorithm in the paper cited above.