In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques.

在本文中，我们研究了一种基于离散动量共识的优化（Momentum-CBO）算法，该算法对应于离散一阶 CBO [S.-Y. Ha、S. Jin 和 D. Kim，基于一阶共识的全局优化算法的收敛性，数学。模型方法应用。科学。 30（2020）2417–2444]。所提出的算法可以理解为ADAM-CBO的修改，用unity代替归一化项。对于所提出的 Momentum-CBO，我们提供了一个足够的框架，保证算法收敛到目标函数的全局最小值。此外，我们提出的几个实验结果表明，与 vanilla-CBO 相比，Momentum-CBO 具有更高的找到全局最小值的成功率，并显示了 Momentum-CBO 在不同初始化方案下的稳定性。我们还表明 Momentum-CBO 可以用作 ADAM-CBO 的替代方案，后者没有适当的收敛分析。最后，我们使用符号回归技术给出了 Momentum-CBO 在 Lyapunov 函数逼近中的应用。