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

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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.

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Acknowledgments

I would like to thank Professor Dianne P. O’Leary and two anonymous referees for careful review of the manuscript and insightful advices to enhance the convergence analysis.

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  1. KCG Holdings, 545 Washington BLVD, Jersey City, NJ, 07310, USA

    Sungwoo Park

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  1. Sungwoo Park
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Correspondence to Sungwoo Park.

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Park, S. A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence . J Optim Theory Appl 170, 512–527 (2016). https://doi.org/10.1007/s10957-016-0917-y

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  • DOI: https://doi.org/10.1007/s10957-016-0917-y

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