We prove non-asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithmin 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 onan arbitrary convex set. In particular the potential is not assumed to be gradient Lipschitz,in contrast with most (if not all) existing works on the topic.

翻译：在Langevin Monte Carlo算法的趋同上,我们证明这种可能性是全球范围内Lipschitz的直线函数,通常是在任意的直线形形形形形形形形形形形形形形形色色的有限数等同函数的最大限度。 特别是,与大多数(如果不是全部的话)关于这个专题的现有工作相比,我们并不认为这种可能性是梯度式的Lipschitz。