An augmented Lagrangian filter method

Sven Leyffer () and Charlie Vanaret ()
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Sven Leyffer: Argonne National Laboratory
Charlie Vanaret: Fraunhofer ITWM

Mathematical Methods of Operations Research, 2020, vol. 92, issue 2, No 5, 343-376

Abstract: Abstract We introduce a filter mechanism to enforce convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows for equality-constrained quadratic programming steps to accelerate local convergence. We also include a feasibility restoration phase that allows fast detection of infeasible problems. We provide a convergence proof that shows that our algorithm converges to first-order stationary points. We provide preliminary numerical results that demonstrate the effectiveness of our proposed method.

Keywords: Augmented Lagrangian; Filter methods; Nonlinear optimization; 90C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-020-00713-x

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