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A nonmonotone filter method for nonlinear optimization

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Abstract

We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a standard, global g-filter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local convergence. A special feature of the proposed method is that it does not require second-order correction steps. We present preliminary numerical results comparing our implementation with a classical filter SQP method.

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Authors and Affiliations

  1. Department of Applied Mathematics, Shanghai Finance University, Shanghai, 201209, China

    Chungen Shen

  2. Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439, USA

    Sven Leyffer

  3. Mathematics Department, University of Dundee, Dundee, UK

    Roger Fletcher

Authors
  1. Chungen Shen
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  2. Sven Leyffer
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  3. Roger Fletcher
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Correspondence to Sven Leyffer.

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Shen, C., Leyffer, S. & Fletcher, R. A nonmonotone filter method for nonlinear optimization. Comput Optim Appl 52, 583–607 (2012). https://doi.org/10.1007/s10589-011-9430-2

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  • DOI: https://doi.org/10.1007/s10589-011-9430-2

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