Sparsity in sums of squares of polynomials

Masakazu Kojima, Sunyoung Kim, Hayato Waki

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

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
Volume103
Issue number1
DOIs
Publication statusPublished - May 1 2005

Fingerprint

Sum of squares
Sparsity
Sparse Polynomials
Polynomials
Polynomial
Semidefinite Programming Relaxation
Multivariate Polynomials
Redundancy
Non-negative
Optimization Problem
Optimization

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Cite this

Sparsity in sums of squares of polynomials. / Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato.

In: Mathematical Programming, Vol. 103, No. 1, 01.05.2005, p. 45-62.

Research output: Contribution to journalArticle

Kojima, Masakazu ; Kim, Sunyoung ; Waki, Hayato. / Sparsity in sums of squares of polynomials. In: Mathematical Programming. 2005 ; Vol. 103, No. 1. pp. 45-62.
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