Yuzhu Wang

Evaluating approximations of the semidefinite cone with trace normalized distance

  • Yuzhu Wang
  • Akiko Yoshise
    • Categories Semi-definite Programming Tags , ,

    We evaluate the dual cone of the set of diagonally dominant matrices (resp., scaled diagonally dominant matrices), namely ${\cal DD}_n^*$ (resp., ${\cal SDD}_n^*$), as an approximation of the semidefinite cone. We prove that the norm normalized distance, proposed by Blekherman et al. (2022), between a set ${\cal S}$ and the semidefinite cone has the same … Read more

    Polyhedral approximations of the semidefinite cone and their application

  • Akihiro Tanaka
  • Yuzhu Wang
  • Akiko Yoshise
    • Categories Linear, Cone and Semidefinite Programming

    We develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded … Read more