  We present convergence and error estimates of the time-discrete
consensus-based optimization(CBO) algorithms proposed in [arXiv:1909.09249] for
general nonconvex functions. In authors' recent work [arxiv: 1910.08239],
rigorous error analysis of the first-order consensus-based optimization
algorithm proposed in [arXiv:1909.09249] was studied at the particle level
without resorting to the kinetic equation via a mean-field limit. However, the
error analysis for the corresponding time-discrete algorithm was not done
mainly due to lack of discrete analogue of It\^o's stochastic calculus. In this
paper, we provide a simple and elementary convergence and error analysis for a
general time-discrete consensus-based optimization algorithm, which includes
the three discrete algorithms in [arXiv:1909.09249]. Our analysis provides
numerical stability and convergence conditions for the three algorithms, as
well as error estimates to the global minimum.
