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Active-set Newton methods for mathematical programs with vanishing constraints

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Abstract

Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious difficulties in theoretical and numerical treatment of these problems. In this work, we suggest several globalization strategies for the active-set Newton-type methods developed earlier by the authors for this problem class, preserving superlinear convergence rate of these methods under weak assumptions. Preliminary numerical results demonstrate that our approach is rather promising and competitive with respect to the existing alternatives.

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Acknowledgements

The authors thank the anonymous referees for useful comments. In particular, Remark 4.1 is in response to the question raised by one of the referees.

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Authors and Affiliations

  1. VMK Faculty, OR Department, Moscow State University, MSU, Uchebniy Korpus 2, Leninskiye Gory, 119991, Moscow, Russia

    A. F. Izmailov & A. L. Pogosyan

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  1. A. F. Izmailov
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  2. A. L. Pogosyan
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Correspondence to A. L. Pogosyan.

Additional information

This research is supported by the Russian Foundation for Basic Research Grant 10-01-00251.

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Izmailov, A.F., Pogosyan, A.L. Active-set Newton methods for mathematical programs with vanishing constraints. Comput Optim Appl 53, 425–452 (2012). https://doi.org/10.1007/s10589-012-9467-x

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