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.

Lasserre hierarchy, Polynomial optimization, Semidefinite optimization, Simulated annealing
Mathematics of Operations Research
Networks and Optimization

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