缓慢增长势中的退火扩散
Annealing diffusions in a slowly growing potential
摘要：
我们考虑一个连续的模拟退火算法在$R^d$。我们证明了收敛的结果，假设弱于通常的。特别是，我们涵盖的情况下，梯度的潜力去为零，在无穷大。证明遵循L. Miclo，但我们用弱Poincaré不等式代替Poincaré和log-Sobolev不等式（在我们的设置中不成立）。我们估计后者与测量能力的标准。我们表明，尽管没有一个频谱间隙，收敛仍然成立的“经典”时间表t = c/ ln（t），如果c是大于一个常数有关的潜力。
英文摘要：
We consider a continuous analogue of the simulated annealing algorithm in $R^d$. We prove a convergence result, under hypotheses weaker than the usual ones. In particular, we cover cases where the gradient of the potential goes to zero at infinity. The proof follows an idea of L. Miclo, but we replace the Poincaré and log-Sobolev inequalities (which do not hold in our setting) by weak Poincaré inequalities. We estimate the latter with measure-capacity criteria. We show that, despite the absence of a spectral gap, the convergence still holds for the "classical" schedule t = c/ ln(t), if c is bigger than a constant related to the potential.
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