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Line search filter methods for nonlinear programming: local convergence. (English) Zbl 1115.90056
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.
MSC:
90C30Nonlinear programming
49M37Methods of nonlinear programming type in calculus of variations
65K05Mathematical programming (numerical methods)
90C55Methods of successive quadratic programming type