Local Convergence of Filter Methods for Equality Constrained Nonlinear Programming

In [10] we discuss general conditions to ensure global convergence of inexact restoration filter algorithms for nonlinear programming. In this paper we show how to avoid the Maratos effect by means of a second order correction. The algorithms are based on feasibility and optimality phases, which can be either independent or not. The optimality phase differs from the original one only when a full Newton step for the tangential minimization of the Lagrangian is efficient but not acceptable by the filter method. In this case a second order corrector step tries to produce an acceptable point keeping the efficiency of the rejected step. The resulting point is tested by trust region criteria. Under usual hypotheses, the algorithm inherits the quadratic convergence properties of the feasibility and optimality phases. The paper includes a comparison between classical SQP and Inexact Restoration iterations, showing that both methods share the same asymptotic convergence properties.