The $\mathbf {K}$-moment problem for continuous linear functionals

DOI10.1090/S0002-9947-2012-05701-1zbMath1275.44003arXiv1102.5763OpenAlexW2963586526MaRDI QIDQ2838073

Jean-Bernard Lasserre

Publication date: 8 July 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5763

zbMATH Keywords

moment problemsreal algebraic geometrypositive polynomialssemi-algebraic sets

Mathematics Subject Classification ID

Polynomials over commutative rings (13B25) Moment problems (44A60) Semialgebraic sets and related spaces (14P10) Polynomials and rational functions of one complex variable (30C10)

Related Items (9)

Projective limit techniques for the infinite dimensional moment problem ⋮ Moment problem in infinitely many variables ⋮ Computing Gaussian \& exponential measures of semi-algebraic sets ⋮ Distributionally robust optimization with polynomial densities: theory, models and algorithms ⋮ Distributionally robust polynomial chance-constraints under mixture ambiguity sets ⋮ Infinite dimensional moment problem: open questions and applications ⋮ The full infinite dimensional moment problem on semi-algebraic sets of generalized functions ⋮ The full moment problem on subsets of probabilities and point configurations ⋮ Moment problem for symmetric algebras of locally convex spaces

Uses Software

• GloptiPoly

Cites Work

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• SOS approximations of nonnegative polynomials via simple high degree perturbations
• Positive cones in enveloping algebras
• The \(K\)-moment problem for compact semi-algebraic sets
• Positive definite functions on Abelian semigroups
• The moment problem for continuous positive semidefinite linear functionals
• Sufficient conditions for a real polynomial to be a sum of squares
• There are significantly more nonnegative polynomials than sums of squares
• The moment problem for non-compact semialgebraic sets
• Positivity, sums of squares and the multi-dimensional moment problem
• GloptiPoly 3: moments, optimization and semidefinite programming
• Semidefinite Programming
• Positivity, sums of squares and the multi-dimensional moment problem II

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