About: Sum-of-squares optimization

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A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables. These constraints are of the form that when the decision variables are used as coefficients in certain polynomials, those polynomials should have the polynomial SOS property. When fixing the maximum degree of the polynomials involved, sum-of-squares optimization is also known as the Lasserre hierarchy of relaxations in semidefinite programming.

Attributes	Values
rdfs:label	Sum-of-squares optimization (en)
rdfs:comment	A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables. These constraints are of the form that when the decision variables are used as coefficients in certain polynomials, those polynomials should have the polynomial SOS property. When fixing the maximum degree of the polynomials involved, sum-of-squares optimization is also known as the Lasserre hierarchy of relaxations in semidefinite programming. (en)
dcterms:subject	Real algebraic geometry Mathematical optimization
Wikipage page ID	30474456 (xsd:integer)
Wikipage revision ID	1103954740 (xsd:integer)
Link from a Wikipage to another Wikipage	Real algebraic geometry Quadratic forms GNU GPL Constraint (mathematics) Duality (optimization) Least squares Gram matrix Mathematical optimization Augmented Lagrangian method Positive-semidefinite matrix Optimization Loss function Polynomial SOS Semidefinite programming Polynomials dbr:Arxiv:1310.4716
Link from a Wikipage to an external page	https://github.com/JuliaOpt/JuMP.jl http://www.cds.caltech.edu/sostools/ http://homepages.laas.fr/henrion/software/gloptipoly/ https://github.com/JuliaOpt/SumOfSquares.jl https://github.com/lanl-ansi/MomentOpt.jl https://github.com/oxfordcontrol/CDCS https://github.com/oxfordcontrol/CDCS/tree/master/packages/%2Bcdcs_sos https://github.com/peterwittek/ncpol2sdpa https://github.com/wangjie212/TSSOS
sameAs	Sum-of-squares optimization Sum-of-squares optimization Sum-of-squares optimization
dbp:wikiPageUsesTemplate	dbt:Hatnote dbt:Main dbt:NumBlk dbt:EquationRef dbt:EquationNote
has abstract	A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables. These constraints are of the form that when the decision variables are used as coefficients in certain polynomials, those polynomials should have the polynomial SOS property. When fixing the maximum degree of the polynomials involved, sum-of-squares optimization is also known as the Lasserre hierarchy of relaxations in semidefinite programming. Sum-of-squares optimization techniques have been applied across a variety of areas, including control theory (in particular, for searching for polynomial Lyapunov functions for dynamical systems described by polynomial vector fields), statistics, finance and machine learning. (en)
prov:wasDerivedFrom	wikipedia-en:Sum-of-squares_optimization?oldid=1103954740&ns=0
page length (characters) of wiki page	16334 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sum-of-squares_optimization
is Link from a Wikipage to another Wikipage of	List of named matrices List of numerical analysis topics Hamilton–Jacobi–Bellman equation Hilbert's seventeenth problem X264 Polynomial SOS Flag algebra Sum of squares SOS-convexity Sum-of-Squares Optimization Sum of squares hierarchy Sum of squares optimization Lasserre hierarchy
is Wikipage redirect of	Sum-of-Squares Optimization Sum of squares hierarchy Sum of squares optimization Lasserre hierarchy
is foaf:primaryTopic of	wikipedia-en:Sum-of-squares_optimization

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