Moments, Positive Polynomials And Their Applications

By Jean B. Lasserre. 2009

1,158 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/af14723d697e77bb1e57d7d83c9c76619711a9e9

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Convex Computation of the Region of Attraction of Polynomial Control Systems (2012, methodology): “Since it is based on (an extension of) Lasserre’s hierarchy of LMI relaxations (originally proposed for static polynomial optimization [26]), our approach scales similarly as Lasserre’s approach.”
Certifiably Optimal Low Rank Factor Analysis (2016, methodology): “One such approach is the method of moments (Lasserre, 2009).”
Semi-algebraic Approximation Using Christoffel–Darboux Kernel (2019, methodology): “turns out that it can also be used for eective computation as it ts perfectly the LP-based methodology described in [16] and the Moment-SOS (polynomial sums of squares) methodology described in e.g. [23, 21, 22]. In the latter methodology one may thus approximate the optimal solution of the measure-”
Sums of squares of polynomials with rational coefficients (2012, positive): “Lasserre’s method of moment relaxation [13] gives, in principle, positivity certiﬁcates for real polynomials based on sum-of-squares decompositions.”
Dead‐beat regulation of mechanical juggling systems (2018, neutral): “By [22,23], one has that the polynomial b(t, χ) has no zero for t ∈ [0, δT ] if and only if the polynomial b̂(v, χ) has no zero for v ∈ (−∞,∞).”
Application of the Moment-SOS Approach to Global Optimization of the OPF Problem (2013, background): “We first review some theoretical aspects of the moment-sos approach (a nice short account can be found in [25], and more in [26] and [27]).”
Amoebas, nonnegative polynomials and sums of squares supported on circuits (2014, background): “For an introduction of nonnegative polynomials and sums of squares, see [3,21,22].”
On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport (2018, background): “This approach concerns a large class of generalized moment problems [22] and can be adapted to deal with special instances of (1) [9].”
Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems (2015, methodology): “which provide nested sequences outer-approximations as hierarchies of linear matrix inequality (LMI) relaxations (Lasserre, 2009); see also Parrilo (2003).”
Optimality conditions and finite convergence of Lasserre’s hierarchy (2012, background): “We refer to [12, 14] for surveys in this area.”