We consider the problem of minimizing a continuous function f over a compact set K. We compare the hierarchy of upper bounds proposed by Lasserre [Lasserre JB (2011) A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21(3):864–885] to bounds that may be obtained from simulated annealing. We show that, when f is a polynomial and 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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Keywords Lasserre hierarchy, Polynomial optimization, Semidefinite optimization, Simulated annealing
Persistent URL dx.doi.org/10.1287/moor.2017.0906
Journal Mathematics of Operations Research
de Klerk, E, & Laurent, M. (2018). Comparison of Lasserre's measure-based bounds for polynomial optimization to bounds obtained by simulated annealing. Mathematics of Operations Research, 43(4), 1317–1325. doi:10.1287/moor.2017.0906