Algorithm 925: Parallel Solver for Semidefinite Programming Problem having Sparse Schur Complement Matrix: SDPARA: SemiDefinite Programming Algorithm paRAllel version. The SDPA (SemidDefinite Programming Algorithm) is known as efficient computer software based on the primal–dual interior-point method for solving SDPs (SemiDefinite Programs). In many applications, however, some SDPs become larger and larger, too large for the SDPA to solve on a single processor. In execution of the SDPA applied to large scale SDPs, the computation of the so-called Schur complement matrix and its Cholesky factorization consume most of the computational time. The SDPARA (SemiDefinite Programming Algorithm paRAllel version) is a parallel version of the SDPA on multiple processors and distributed memory, which replaces these two parts by their parallel implementation using MPI and ScaLAPACK. Through numerical results, we show that the SDPARA on a PC cluster consisting of 64 processors attains high scalability for large scale SDPs without losing the stability of the SDPA.

References in zbMATH (referenced in 18 articles , 1 standard article )

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  1. Dickinson, Peter J. C.; Povh, Janez: A new approximation hierarchy for polynomial conic optimization (2019)
  2. Korda, Milan; Jones, Colin N.: Stability and performance verification of optimization-based controllers (2017)
  3. Fujisawa, Katsuki; Endo, Toshio; Yasui, Yuichiro: Advanced computing and optimization infrastructure for extremely large-scale graphs on post peta-scale supercomputers (2016) ioport
  4. Wittek, Peter: Algorithm 950: Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables (2015)
  5. Gawlitza, Thomas Martin; Seidl, Helmut; Adjé, Assalé; Gaubert, Stéphane; Goubault, Éric: Abstract interpretation meets convex optimization (2012)
  6. Koch, Thorsten; Ralphs, Ted; Shinano, Yuji: Could we use a million cores to solve an integer program? (2012)
  7. Sivaramakrishnan, Kartik Krishnan; Mitchell, John E.: Properties of a cutting plane method for semidefinite programming (2012)
  8. Yamashita, Makoto; Fujisawa, Katsuki; Fukuda, Mituhiro; Kobayashi, Kazuhiro; Nakata, Kazuhide; Nakata, Maho: Latest developments in the SDPA family for solving large-scale SDPs (2012)
  9. Yamashita, Makoto; Fujisawa, Katsuki; Fukuda, Mituhiro; Nakata, Kazuhide; Nakata, Maho: Algorithm 925, parallel solver for semidefinite programming problem having sparse Schur complement matrix (2012)
  10. Ivanov, I. D.; de Klerk, E.: Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster (2010)
  11. Sivaramakrishnan, Kartik Krishnan: A parallel interior point decomposition algorithm for block angular semidefinite programs (2010)
  12. Peña, Javier F.; Vera, Juan C.; Zuluaga, Luis F.: Exploiting equalities in polynomial programming (2008)
  13. Borchers, Brian; Young, Joseph G.: Implementation of a primal-dual method for SDP on a shared memory parallel architecture (2007)
  14. Fujisawa, Katsuki; Nakata, Kazuhide; Yamashita, Makoto; Fukuda, Mituhiro: SDPA project: solving large-scale semidefinite programs (2007)
  15. Fukuda, Mituhiro; Braams, Bastiaan J.; Nakata, Maho; Overton, Michael L.; Percus, Jerome K.; Yamashita, Makoto; Zhao, Zhengji: Large-scale semidefinite programs in electronic structure calculation (2007)
  16. Nayakkankuppam, Madhu V.: Solving large-scale semidefinite programs in parallel (2007)
  17. Fujisawa, Katsuki; Fukuda, Mituhiro; Nakata, Kazuhide: Preprocessing sparse semidefinite programs via matrix completion (2006)
  18. Fujisawa, Katsuki; Kojima, Masakazu; Takeda, Akiko; Yamashita, Makoto: Solving large scale optimization problems via grid and cluster computing (2004)