Sparsity in sums of squares of polynomials

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 met...

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Bibliographic Details
Published inMathematical programming Vol. 103; no. 1; pp. 45 - 62
Main Authors Kojima, Masakazu, Kim, Sunyoung, Waki, Hayato
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.05.2005
Springer Nature B.V
Subjects
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization
Polynomials
Sparsity
Studies
Semidefinite program
Semidefinite relaxation
Sparsity
Redundancy
Sparse matrix
Semi definite programming
Polynomial optimization problem
Optimization
Sums of squares of polynomial
Mathematical programming
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ISSN0025-5610
1436-4646
DOI10.1007/s10107-004-0554-3

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Summary: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. [PUBLICATION ABSTRACT]
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-004-0554-3