6 problems

The paper considers second-order particle-swarm-optimization dynamics and a kinetic BGK model obtained in a mean-field limit. In the setting of non-degenerate Gaussian noise and a…

Convergence-rate conjecture. The formula $\mathcal{C}[f_n]$ converges in the following cases, with the indicated rates:

Polynomial-bounded convergence conjecture. The convergence rate is likely to be polynomial-bounded under mild assumptions, extending beyond the condition required by the cited anal…

Geometric convergence conjecture. The geometric convergence rate at equation $$ may still hold when $m>2$.

Let a Gaussian mixture model have $K$ components with minimum mixing weight $pi_{\min}$, and let $R_{\min}$ denote the minimum separation and $R_i$ the separation associated with c…

Let $K$ and $U$ be the sets in the preceding convergence setting, with $U$ intersecting the interior of $K$. The circumcentered-reflection method (CRM) generates an iterative seque…