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

Article

## 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.

## Keywords

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

## Mathematical Subject Classification (2000):

49M37 65K05 90C30 90C51

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