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Active-set Newton methods for mathematical programs with vanishing constraints

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  • A. Izmailov
  • A. Pogosyan

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • A. Izmailov & A. Pogosyan, 2012. "Active-set Newton methods for mathematical programs with vanishing constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 425-452, October.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:425-452
    DOI: 10.1007/s10589-012-9467-x
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    References listed on IDEAS

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    1. A. F. Izmailov & M. V. Solodov, 2009. "Mathematical Programs with Vanishing Constraints: Optimality Conditions, Sensitivity, and a Relaxation Method," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 501-532, September.
    2. A. Izmailov & A. Pogosyan & M. Solodov, 2012. "Semismooth Newton method for the lifted reformulation of mathematical programs with complementarity constraints," Computational Optimization and Applications, Springer, vol. 51(1), pages 199-221, January.
    3. Y. D. Chen & Y. Gao & Y.-J. Liu, 2010. "An Inexact SQP Newton Method for Convex SC1 Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 33-49, July.
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    Cited by:

    1. S. K. Mishra & Vinay Singh & Vivek Laha, 2016. "On duality for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 243(1), pages 249-272, August.

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