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Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems

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  • Renato Monteiro
  • Camilo Ortiz
  • Benar Svaiter

Abstract

In this paper, we consider block-decomposition first-order methods for solving large-scale conic semidefinite programming problems given in standard form. Several ingredients are introduced to speed-up the method in its pure form such as: an aggressive choice of stepsize for performing the extragradient step; use of scaled inner products; dynamic update of the scaled inner product for properly balancing the primal and dual relative residuals; and proper choices of the initial primal and dual iterates, as well as the initial parameter for the scaled inner product. Finally, we present computational results showing that our method outperforms the two most competitive codes for large-scale conic semidefinite programs, namely: the boundary-point method introduced by Povh et al. and the Newton-CG augmented Lagrangian method by Zhao et al. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Renato Monteiro & Camilo Ortiz & Benar Svaiter, 2014. "Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems," Computational Optimization and Applications, Springer, vol. 57(1), pages 45-69, January.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:45-69
    DOI: 10.1007/s10589-013-9590-3
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    Cited by:

    1. Maicon Marques Alves & Samara Costa Lima, 2017. "An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 818-847, December.
    2. Maicon Marques Alves & B. F. Svaiter, 2016. "A Variant of the Hybrid Proximal Extragradient Method for Solving Strongly Monotone Inclusions and its Complexity Analysis," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 198-215, January.
    3. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.

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