Sparsity in sums of squares of polynomials

Masakazu Kojima, Sunyoung Kim, Hayato Waki

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming (SDP) relaxation of polynomial optimization problems. We discuss effective methods to obtain a simpler representation of a "sparse" polynomial as a sum of squares of sparse polynomials by eliminating redundancy.

Original languageEnglish
Pages (from-to)45-62
Number of pages18
JournalMathematical Programming
Issue number1
StatePublished - May 2005


  • Polynomial optimization problem
  • Semidefinite program
  • Sparsity
  • Sums of squares of polynomial


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