### 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 language | English |
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Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Mathematical Programming |

Volume | 103 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

### Cite this

*Mathematical Programming*,

*103*(1), 45-62. https://doi.org/10.1007/s10107-004-0554-3

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

Research output: Contribution to journal › Article

*Mathematical Programming*, vol. 103, no. 1, pp. 45-62. https://doi.org/10.1007/s10107-004-0554-3

}

TY - JOUR

T1 - Sparsity in sums of squares of polynomials

AU - Kojima, Masakazu

AU - Kim, Sunyoung

AU - Waki, Hayato

PY - 2005/5/1

Y1 - 2005/5/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=17444428545&partnerID=8YFLogxK

U2 - 10.1007/s10107-004-0554-3

DO - 10.1007/s10107-004-0554-3

M3 - Article

VL - 103

SP - 45

EP - 62

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -