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An augmented Lagrangian filter method

Author

Listed:
  • Sven Leyffer

    (Argonne National Laboratory)

  • Charlie Vanaret

    (Fraunhofer ITWM)

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.

Suggested Citation

  • Sven Leyffer & Charlie Vanaret, 2020. "An augmented Lagrangian filter method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 343-376, October.
    • Handle: RePEc:spr:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00713-x
    DOI: 10.1007/s00186-020-00713-x
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    References listed on IDEAS

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