Sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity

Hayato Waki, Sunyoung Kim, Masakazu Kojima, Masakazu Muramatsu

Research output: Contribution to journalArticle

230 Citations (Scopus)


Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of the supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite program (SDP) relaxations are obtained. Numerical results from various test problems are included to show the improved performance of the SOS and SDP relaxations.

Original languageEnglish
Pages (from-to)218-242
Number of pages25
JournalSIAM Journal on Optimization
Issue number1
Publication statusPublished - Feb 26 2007
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

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