Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization

Hayato Waki, Maho Nakata, Masakazu Muramatsu

Research output: Contribution to journalArticle

17 Citations (Scopus)


We observe that in a simple one-dimensional polynomial optimization problem (POP), the 'optimal' values of semidefinite programming (SDP) relaxation problems reported by the standard SDP solvers converge to the optimal value of the POP, while the true optimal values of SDP relaxation problems are strictly and significantly less than that value. Some pieces of circumstantial evidences for the strange behaviors of the SDP solvers are given. This result gives a warning to users of the SDP relaxation method for POPs to be careful in believing the results of the SDP solvers. We also demonstrate how SDPA-GMP, a multiple precision SDP solver developed by one of the authors, can deal with this situation correctly.

Original languageEnglish
Pages (from-to)823-844
Number of pages22
JournalComputational Optimization and Applications
Issue number3
Publication statusPublished - Jan 1 2012
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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