Before revision:  Based on an experimentally supported intuition that CBO  performs a gradient descent on the convex envelope of a given objective , we derive a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions.
After revision:  Based on an experimentally supported intuition that CBO performs a gradient descent of the squared Euclidean distance to the global minimizer , we derive a novel technique for proving the convergence to the global minimizer in mean-field law for a rich class of objective functions.