Andreas Wachter

This paper is the basis of the highly successful code IPOPT for nonlinear programming. This open-source software package, which is one of the most advanced codes for large-scale nonlinear programming, is the first to combine a barrier nonlinear programming method with a line search filter method, with a fundamental convergence theory for this approach. The result is an efficient, large-scale nonlinear programming code with global convergence properties and fast local convergence properties under weak assumptions. As described in the paper, IPOPT includes a number of refinements that overcome the Maratos effect (slow convergence) and effectively deal with negative curvature and rank deficiency in nonlinear problems. Moreover, it strongly leverages recent advances in automatic differentiation for first and second derivatives along with indefinite factorizations of large, sparse matrices. In independent tests IPOPT has consistently performed among the top state-of-the-art nonlinear programming solvers. IPOPT is available freely, is easy to use, and has interfaces to many modeling packages. As a result, it makes large-scale nonlinear programming accessible to a broad audience.