亚稳环境中的亚稳性和动力学模拟退火

On the convergence of an improved and adaptive kinetic simulated annealing

Inspired by the work of [Fang et al.. An improved annealing method and its large-time behaviour. Stochastic Process. Appl. (1997), Volume 71 Issue 1 Page 55-74.], who propose an improved simulated annealing algorithm based on a variant of overdamped Langevin diffusion with state-dependent diffusion coefficient, we cast this idea in the kinetic setting and develop an improved kinetic simulated annealing (IKSA) method for minimizing a target function $U$. To analyze its convergence, we utilize the framework recently introduced by [Monmarché. Hypocoercivity in metastable settings and kinetic simu…

弱庞加莱不等式、模拟退火与从球面自旋玻璃中采样

Weak Poincaré Inequalities, Simulated Annealing, and Sampling from Spherical Spin Glasses

本文提出基于弱庞加莱不等式的模拟退火分析框架，并利用局部到全局原则证明该不等式，首次实现球面自旋玻璃在超越唯一性阈值情形下的马尔可夫链采样保证。