Mathematical Methods of Operations Research

, Volume 87, Issue 3, pp 451–483 | Cite as

A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm

  • Renke Kuhlmann
  • Christof Büskens
Original Article


Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal–dual penalty-interior-point algorithm is proposed, that is based on an augmented Lagrangian approach with an \(\ell 2\)-exact penalty function. Global convergence is maintained by a combination of a merit function and a filter approach. Unlike the majority of filter methods, no separate feasibility restoration phase is required. The algorithm has been implemented within the solver WORHP to study different penalty and line search options and to compare its numerical performance to two other state-of-the-art nonlinear programming algorithms, the interior-point method IPOPT and the sequential quadratic programming method of WORHP.


Nonlinear programming Constrained optimization Augmented Lagrangian Penalty-interior-point algorithm Primal–dual method 

Mathematics Subject Classification

49M05 49M15 49M29 49M37 90C06 90C26 90C30 90C51 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Optimization and Optimal Control, Center for Industrial Mathematics (ZeTeM)University of BremenBremenGermany

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