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A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence

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  • Sungwoo Park

    (KCG Holdings)

Abstract

Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O’Leary proposed a constraint-reduced predictor–corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraint-reduced algorithm for semidefinite programming having both polynomial global and superlinear local convergences. The new algorithm repeats a corrector step to have an iterate tangentially approach a central path, by which superlinear convergence can be achieved. This study proves its convergence rate and shows its effective cost saving in numerical experiments.

Suggested Citation

  • Sungwoo Park, 2016. "A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 512-527, August.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:2:d:10.1007_s10957-016-0917-y
    DOI: 10.1007/s10957-016-0917-y
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    References listed on IDEAS

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    1. F. A. Potra & R. Sheng, 1998. "Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 103-119, October.
    2. Sungwoo Park & Dianne P. O’Leary, 2015. "A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 558-571, August.
    3. Jin Jung & Dianne O’Leary & André Tits, 2012. "Adaptive constraint reduction for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 51(1), pages 125-157, January.
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    Cited by:

    1. M. Paul Laiu & André L. Tits, 2019. "A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme," Computational Optimization and Applications, Springer, vol. 72(3), pages 727-768, April.

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