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This paper investigates the behavior of PSO (particle swarm optimization) and CMA-ES (covariance matrix adaptation evolution strategy) on ill-conditioned functions. The paper also highlights momentum as important common concept used in both algorithms and reviews important invariance properties. On separable, ill-conditioned functions, PSO performs very well and outperforms CMA-ES by a factor of up to five. On the same but rotated functions, the performance of CMA-ES is unchanged, while the performance of PSO declines dramatically: on non-separable, ill-conditioned functions we find the search costs (number of function evaluations) of PSO increasing roughly proportional with the condition number and CMA-ES outperforms PSO by orders of magnitude. The strong dependency of PSO on rotations originates from random events that are only independent within the given coordinate system. The CMA-ES …