We prove non asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of affine functions on an arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz, in contrast with most existing works on the topic.

翻译：在Langevin Monte Carlo算法合而为一的情况下,我们证明,在这种情况下,潜力是全球范围内Lipschitz的直线函数,通常是在任意的直线组合上有限数目的直线函数的上限。 特别是,与大多数关于这个专题的现有工作相比,我们并不认为潜力是梯度的Lipschitz。