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arXiv · 1703.00744

Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing

Etienne de Klerk·Monique Laurent
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Abstract

Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing. We consider the problem of minimizing a continuous function $f$ over a compact set $\mathbf{K}$. We compare the hierarchy of upper bounds proposed by Lasserre in [{\em SIAM J. Optim.} $21(3)$ $(2011)$, pp. $864-885$] to bounds that may be obtained from simulated annealing. We show that, when $f$ is a polynomial and $\mathbf{K}$ a convex body, this comparison yields a faster rate of convergence of the Lasserre hierarchy than what was previously known in the literature.

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Etienne de Klerk, Monique Laurent. 2017-03-02. Comparison of Lasserre's measure--based bounds for polynomial optimization to bounds obtained by simulated annealing. https://arxiv.org/abs/1703.00744

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