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A primal-dual augmented Lagrangian penalty-interior-point filter line search algorithm. (English) Zbl 1394.49025
Summary: 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.

MSC:
49M05 Numerical methods based on necessary conditions
49M15 Newton-type methods
49M29 Numerical methods involving duality
49M37 Numerical methods based on nonlinear programming
90C06 Large-scale problems in mathematical programming
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C51 Interior-point methods
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