In this paper, the filter technique of Fletcher and Leyffer (1997) is used to globalize the primaldual interior-point algorithm for nonlinear programming, avoiding the use of merit functions and the updating of penalty parameters. The new algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step, whose sizes are controlled by a trust-region type parameter. Each entry in the filter is a pair of coordinates: one resulting from feasibility and centrality, and associated with the normal step; the other resulting from optimality (complementarity and duality), and related with the tangential step. Global convergence to first-order critical points is proved for the new primal-dual interior-point filter algorithm.

Abstract not found

We prove a new local convergence property of a primal-dual method for solving nonlinear optimization problem. Following a standard interior point approach, the complementarity conditions of the original primal-dual system are perturbed by a parameter which is driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed system and by applying the fraction to the boundary rule to maintain strict feasibility of the iterates with respect to the nonnegativity constraints. The analysis of the rate of convergence is carried out by considering a linear or a superlinear arbitrary decreasing sequence of perturbation parameters. We show that, if the perturbation parameters converge to zero linearly or superlinearly and once an iterate belongs to a neighborhood of convergence of the Newton method applied to the original system, then the whole sequence of iterates converges and asymptotically follows the central trajectory in a natural way.