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

Abstract.

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.

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Correspondence to Andreas Wächter.

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Wächter, A., Biegler, L. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–57 (2006). https://doi.org/10.1007/s10107-004-0559-y

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Keywords

  • Nonlinear programming
  • Nonconvex constrained optimization
  • Filter method
  • Line search
  • Interior-point method
  • Barrier method

Mathematical Subject Classification (2000):

  • 49M37
  • 65K05
  • 90C30
  • 90C51