In this talk, we present the primal-dual interior-point filter method for nonlinear programming developed by Ulbrich, Ulbrich, and Vicente (2000). The method is based on the application of the filter technique of Fletcher and Leyffer (1997) to the globalization of the primal-dual interior-point algorithm, avoiding the use of merit functions and the updating of penalty parameters.
The algorithm decomposes the primal-dual step obtained from the perturbed first-order necessary conditions into a normal and a tangential step. 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. The method possesses global convergence to first-order critical points.
We present numerical results for large-scale problems and discuss extensions of the original algorithm and of its convergence theory.
This is joint work with Renata D. Silva, Michael Ulbrich, and Stefan Ulbrich.