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Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming

Author

Listed:
  • S. Cafieri

    (2nd University of Naples)

  • M. D’Apuzzo

    (2nd University of Naples)

  • V. Simone

    (2nd University of Naples)

  • D. Serafino

    (2nd University of Naples)

  • G. Toraldo

    (University of Naples Federico II)

Abstract

We analyze the convergence of an infeasible inexact potential reduction method for quadratic programming problems. We show that the convergence of this method is achieved if the residual of the KKT system satisfies a bound related to the duality gap. This result suggests stopping criteria for inner iterations that can be used to adapt the accuracy of the computed direction to the quality of the potential reduction iterate in order to achieve computational efficiency.

Suggested Citation

  • S. Cafieri & M. D’Apuzzo & V. Simone & D. Serafino & G. Toraldo, 2007. "Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 355-366, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9264-3
    DOI: 10.1007/s10957-007-9264-3
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    References listed on IDEAS

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    1. S. Cafieri & M. D’Apuzzo & M. Marino & A. Mucherino & G. Toraldo, 2006. "Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 55-75, April.
    2. Michael J. Todd & Yinyu Ye, 1990. "A Centered Projective Algorithm for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 508-529, August.
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    Cited by:

    1. Kuo-Ling Huang & Sanjay Mehrotra, 2017. "Solution of Monotone Complementarity and General Convex Programming Problems Using a Modified Potential Reduction Interior Point Method," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 36-53, February.
    2. Marco Viola & Mara Sangiovanni & Gerardo Toraldo & Mario R. Guarracino, 2019. "Semi-supervised generalized eigenvalues classification," Annals of Operations Research, Springer, vol. 276(1), pages 249-266, May.

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