Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Worst-case examples for Lasserre's measure--based hierarchy for
  polynomial optimization on the hypercube   We study the convergence rate of a hierarchy of upper bounds for polynomial
optimization problems, proposed by Lasserre [SIAM J. Optim. 21(3) (2011), pp.
864-885], and a related hierarchy by De Klerk, Hess and Laurent [SIAM J. Optim.
27(1), (2017) pp. 347-367]. For polynomial optimization over the hypercube, we
show a refined convergence analysis for the first hierarchy. We also show lower
bounds on the convergence rate for both hierarchies on a class of examples.
These lower bounds match the upper bounds and thus establish the true rate of
convergence on these examples. Interestingly, these convergence rates are
determined by the distribution of extremal zeroes of certain families of
orthogonal polynomials.

25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an