Lucas Slot

activity

20192026

most citedImproved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets

21 citations · 50 across the 18 of their papers we have counts for

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Showing 2021Show all

3 papers · 1 filter

math.OC2021

Sum-of-squares hierarchies for polynomial optimization and the Christoffel-Darboux kernel

Lucas Slot

Consider the problem of minimizing a polynomial $f$ over a compact semialgebraic set $X \subseteq R^{n}$ . Lasserre introduces hierarchies of semidefinite programs…

math.OC2021★ 1 cited

An effective version of Schmüdgen's Positivstellensatz for the hypercube

Monique Laurent, Lucas Slot

Let $S \subseteq R^{n}$ be a compact semialgebraic set and let $f$ be a polynomial nonnegative on $S$ . Schmüdgen's Positivstellensatz then states that for any $η > 0$ , the no…

math.CO2021★ 1 cited

A recursive Lovász theta number for simplex-avoiding sets

Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot +1

We recursively extend the Lovász theta number to geometric hypergraphs on the unit sphere and on Euclidean space, obtaining an upper bound for the independence ratio of these hyper…