We introduce a new consensus based optimization (CBO) method where interacting particle system is driven by jump-diffusion stochastic differential equations. We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.

翻译：我们采用了一种新的基于共识的优化(CBO)方法,通过这种方法,互动粒子系统是由跳式扩散随机差异方程式驱动的;我们研究了粒子系统及其平均场限的稳妥性;本文件的主要贡献是证明了互动粒子系统与平均场限的趋同性,以及离散粒系统与平均平方值的连续时间动态的趋同;我们还证明,平均场跳式扩散SDE系统与大量客观功能的全球最小化系统相趋一致。我们证明,在基准目标功能的数字模拟中,拟议的CBO方法比早期CBO方法的性能有所提高。