Comparison of Lasserre’s Measure-Based Bounds for Polynomial Optimization to Bounds Obtained by Simulated Annealing
比较了Lasserre提出的多项式优化上界层次结构与模拟退火得到的界，发现当目标函数为多项式且可行域为凸体时，Lasserre层次结构的收敛速度比文献中已知的更快。
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.