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pro vyhledávání: '"Lasserre, Jean B."'
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 361, Iss G5, Pp 935-952 (2023)
We first interpret Pell’s equation satisfied by Chebyshev polynomials for each degree $t$, as a certain Positivstellensatz, which then yields for each integer $t$, what we call a generalized Pell’s equation, satisfied by reciprocals of Christoffe
Externí odkaz:
https://doaj.org/article/18ca7a2c09c34378948a07ad629a7da0
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G8, Pp 919-928 (2022)
We show that the empirical Christoffel function associated with a cloud of finitely many points sampled from a distribution, can provide a simple tool for supervised classification in data analysis, with good generalization properties.
Externí odkaz:
https://doaj.org/article/29fbb5144fc84811ba12e678dc8a55b9
Autor:
Lasserre, Jean B.
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G9, Pp 1071-1079 (2022)
We show that the Christoffel function (CF) factorizes (or can be disintegrated) as the product of two Christoffel functions, one associated with the marginal and the another related to the conditional distribution, in the spirit of “the CF of the d
Externí odkaz:
https://doaj.org/article/7933d0edff4d430eb082cc42939c4e37
Autor:
Kozhasov, Khazhgali, Lasserre, Jean B.
Let $\mathcal{C}_{d,n}$ be the convex cone consisting of real $n$-variate degree $d$ forms that are strictly positive on $\mathbb{R}^n\setminus \{\mathbf{0}\}$. We prove that the Lebesgue volume of the sublevel set $\{g\leq 1\}$ of $g\in \mathcal{C}_
Externí odkaz:
http://arxiv.org/abs/2206.05170
We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy -- a moment-SOS based hierarchy that exploits both correlative and term sparsity, which can provide tighter S
Externí odkaz:
http://arxiv.org/abs/2109.10005
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS (sums of squ
Externí odkaz:
http://arxiv.org/abs/2009.12139
This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously correlative sparsity and term sparsity by combining advantages of two existing f
Externí odkaz:
http://arxiv.org/abs/2005.02828
Autor:
Lasserre, Jean B.
Publikováno v:
In Journal of Approximation Theory November 2023 295
Publikováno v:
In Electric Power Systems Research December 2022 213
Autor:
Lasserre, Jean B. *
Publikováno v:
In IFAC PapersOnLine 2022 55(30):383-387