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An SQP method for mathematical programs with vanishing constraints with strong convergence properties

Author

Listed:
  • Matúš Benko

    (Johannes Kepler University Linz)

  • Helmut Gfrerer

    (Johannes Kepler University Linz)

Abstract

We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of $${\mathcal {Q}}$$ Q -stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how $${\mathcal {Q}}_M$$ Q M -stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of $${\mathcal {Q}}_M$$ Q M -stationarity of the limit points.

Suggested Citation

  • Matúš Benko & Helmut Gfrerer, 2017. "An SQP method for mathematical programs with vanishing constraints with strong convergence properties," Computational Optimization and Applications, Springer, vol. 67(2), pages 361-399, June.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9894-9
    DOI: 10.1007/s10589-017-9894-9
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    References listed on IDEAS

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    1. Wolfgang Achtziger & Tim Hoheisel & Christian Kanzow, 2013. "A smoothing-regularization approach to mathematical programs with vanishing constraints," Computational Optimization and Applications, Springer, vol. 55(3), pages 733-767, July.
    2. 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.
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    Cited by:

    1. Qingjie Hu & Jiguang Wang & Yu Chen, 2020. "New dualities for mathematical programs with vanishing constraints," Annals of Operations Research, Springer, vol. 287(1), pages 233-255, April.

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