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Computational Optimization and Applications

, Volume 53, Issue 2, pp 425–452 | Cite as

Active-set Newton methods for mathematical programs with vanishing constraints

  • A. F. Izmailov
  • A. L. Pogosyan
Article

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.

Keywords

Mathematical program with vanishing constraints Constraint qualification Optimality condition Active-set method Sequential quadratic programming Semismooth Newton method Global convergence 

Notes

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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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.VMK Faculty, OR DepartmentMoscow State University, MSUMoscowRussia

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