Mathematical Programming

, Volume 106, Issue 1, pp 25–57

On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming


DOI: 10.1007/s10107-004-0559-y

Cite this article as:
Wächter, A. & Biegler, L. Math. Program. (2006) 106: 25. doi:10.1007/s10107-004-0559-y


We present a primal-dual interior-point algorithm with a filter line-search method for nonlinear programming. Local and global convergence properties of this method were analyzed in previous work. Here we provide a comprehensive description of the algorithm, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Heuristics are also considered that allow faster performance. This method has been implemented in the IPOPT code, which we demonstrate in a detailed numerical study based on 954 problems from the CUTEr test set. An evaluation is made of several line-search options, and a comparison is provided with two state-of-the-art interior-point codes for nonlinear programming.


Nonlinear programmingNonconvex constrained optimizationFilter methodLine searchInterior-point methodBarrier method

Mathematical Subject Classification (2000):


Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.IBM T.J. Watson Research CenterYorktown HeightsUSA
  2. 2.Carnegie Mellon UniversityPittsburghUSA