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Latest Developments in the SDPA Family for Solving Large-Scale SDPs

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Makoto Yamashita

    (Tokyo Institute of Technology)

  • Katsuki Fujisawa

    (Chuo University)

  • Mituhiro Fukuda

    (Tokyo Institute of Technology)

  • Kazuhiro Kobayashi

    (National Maritime Research Institute)

  • Kazuhide Nakata

    (Tokyo Institute of Technology)

  • Maho Nakata

    (RIKEN)

Abstract

The main purpose of this chapter is to introduce the latest developments in SDPA and its family. SDPA is designed to solve large-scale SemiDefinite Programs (SDPs) faster and over the course of 15 years of development, it has been expanded into a high-performance-oriented software package. We hope that this introduction to the latest developments of the SDPA Family will be beneficial to readers who wish to understand the inside of state-of-art software packages for solving SDPs.

Suggested Citation

  • Makoto Yamashita & Katsuki Fujisawa & Mituhiro Fukuda & Kazuhiro Kobayashi & Kazuhide Nakata & Maho Nakata, 2012. "Latest Developments in the SDPA Family for Solving Large-Scale SDPs," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 687-713, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_24
    DOI: 10.1007/978-1-4614-0769-0_24
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    Citations

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    Cited by:

    1. Hikaru Komeiji & Sunyoung Kim & Makoto Yamashita, 2019. "On the conditions for the finite termination of ADMM and its applications to SOS polynomials feasibility problems," Computational Optimization and Applications, Springer, vol. 74(2), pages 317-344, November.
    2. Florian Jarre & Felix Lieder & Ya-Feng Liu & Cheng Lu, 2020. "Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting," Journal of Global Optimization, Springer, vol. 76(4), pages 913-932, April.
    3. Gicquel, C. & Lisser, A. & Minoux, M., 2014. "An evaluation of semidefinite programming based approaches for discrete lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 237(2), pages 498-507.
    4. Masaki Kimizuka & Sunyoung Kim & Makoto Yamashita, 2019. "Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods," Journal of Global Optimization, Springer, vol. 75(3), pages 631-654, November.

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