Global Optimisation in Hilbert Spaces using the Survival of the Fittest Algorithm

The paper’s SoFA kernel is defined with f(r) = −r^2/(2R^2) and then used directly as a “probability density” via (k+1) f(‖z−z̄‖)/∫(k+1) f(‖z−z̄‖), which is negative off the reference point and therefore cannot be a probability density. This flaw appears verbatim in the algorithm (Section 2.1) and in the proofs, where “probabilities” are computed by integrating this negative kernel . Theorem 2 also introduces Gaussian error-function bounds involving √ln(k+1), which are inconsistent with the stated (polynomial/negative) kernel, suggesting an unmotivated switch to an exponential kernel that was never specified . Thus the convergence proof does not hold as written. The candidate model correctly identifies the kernel/sign error, proposes the natural repair (Boltzmann factor exp((k+1)f(·))), and then gives a counterexample showing the claimed “for every continuous J with a unique maximizer” convergence still fails in general because the variance shrinks too fast, leaving positive probability of never entering a maximizer’s neighborhood. Hence, the paper’s claim is false as stated, while the model’s critique and counterexample are sound.