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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| Published in | Mathematical programming Vol. 103; no. 1; pp. 45 - 62 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer
01.05.2005
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0025-5610 1436-4646 |
| DOI | 10.1007/s10107-004-0554-3 |
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| 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. [PUBLICATION ABSTRACT] |
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| AbstractList | 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] |
| Author | Kim, Sunyoung Kojima, Masakazu Waki, Hayato |
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| Cites_doi | 10.1137/1.9781611970777 10.1090/conm/253/03936 10.1007/s10107-003-0387-5 10.1137/S1052623400366802 10.15807/jorsj.46.125 10.1007/BF01070233 10.1016/S0022-4049(97)83827-3 10.1080/1055678031000118482 10.1215/S0012-7094-78-04519-2 10.1137/S1052623400380079 10.1512/iumj.1993.42.42045 10.1080/10556789908805766 10.1080/10556789908805762 |
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| Keywords | 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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