Summary: A line search method is proposed for nonlinear programming using Fletcher and Leyffer’s filter method [R. Flechter
and S. Leyffer
, Math. Program. 91, No. 2 (A), 239–269 (2002; Zbl 1049.90088
)], which replaces the traditional merit function. A simple modification of the method proposed in a companion paper [SIAM J. Optim. 16, No. 1, 1–31 (2005; Zbl 1114.90128
)] introducing second order correction steps is presented. It is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved.