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arXiv · 2003.05086

Convergence and error estimates for time-discrete consensus-based optimization algorithms

Seug-Yeal Ha·Shi Jin·Doheon Kim
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Abstract

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.

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Seug-Yeal Ha, Shi Jin, Doheon Kim. 2020-03-11. Convergence and error estimates for time-discrete consensus-based optimization algorithms. https://arxiv.org/abs/2003.05086

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