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Superlinear Convergence of the Sequential Quadratic Method in Constrained Optimization

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Abstract

This paper pursues a twofold goal. Firstly, we aim at deriving novel second-order characterizations of important robust stability properties of perturbed Karush–Kuhn–Tucker systems for a broad class of constrained optimization problems generated by parabolically regular sets. Secondly, the obtained characterizations are applied to establish well-posedness and superlinear convergence of the basic sequential quadratic programming method to solve parabolically regular constrained optimization problems.

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Acknowledgements

The authors are grateful to two anonymous referees and the handling editor for carefully reading the paper and for their insightful comments that allowed us to improve the original presentation. Research of the first author was partly supported by the US National Science Foundation under grant DMS-1808978 and by the US Air Force Office of Scientific Research under grant #15RT0462. Research of the second author was partly supported by the US National Science Foundation under grants DMS-1512846 and DMS-1808978, by the US Air Force Office of Scientific Research under grant #15RT0462, and by the Australian Research Council Discovery Project DP-190100555.

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Authors and Affiliations

  1. Wayne State University, Detroit, MI, USA

    Ashkan Mohammadi & Boris S. Mordukhovich

  2. Miami University, Oxford, OH, USA

    M. Ebrahim Sarabi

Authors
  1. Ashkan Mohammadi
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  2. Boris S. Mordukhovich
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  3. M. Ebrahim Sarabi
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Correspondence to Boris S. Mordukhovich.

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Communicated by Marcin Studniarski.

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Mohammadi, A., Mordukhovich, B.S. & Sarabi, M.E. Superlinear Convergence of the Sequential Quadratic Method in Constrained Optimization. J Optim Theory Appl 186, 731–758 (2020). https://doi.org/10.1007/s10957-020-01720-y

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