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An Inexact SQP Newton Method for Convex SC1 Minimization Problems

Author

Listed:
  • Y. D. Chen

    (Royal Bank of Scotland, 38/F, Cheung Kong Center)

  • Y. Gao

    (National University of Singapore)

  • Y.-J. Liu

    (Shenyang Institute of Aeronautical Engineering)

Abstract

In this paper, we present a globally and superlinearly convergent inexact SQP Newton method for solving large scale convex SC 1 minimization problems under mild conditions. In particular, the BD-regularity assumption made by Pang and Qi in Journal of Optimization Theory and Applications, 85 (1995), pp. 633–648 is replaced by a much more realistic assumption. Our numerical experiments conducted on least squares semidefinite programming with lower and upper bounds demonstrate that our inexact SQP Newton method is much more efficient than its exact version and is competitive with existing methods when the number of simple constraints is very large.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:1:d:10.1007_s10957-010-9654-9
    DOI: 10.1007/s10957-010-9654-9
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    2. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
    3. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. 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.

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